"The main impression I formed in Trebinje was of how much pain people endured, of the fear they lived in every single day. That's something you can't properly convey to anyone, and I'm just grateful I didn't have to go through it. My family made the right decision."
But the jolting reacquaintance with his past stirred an impulse in Begovic to forge a deeper connection. Propitiously, in 2009, the chance arrived, as the new Bosnian international soccer team enabled him to reaffirm his sense of belonging.
Every time he lands at Sarajevo airport for a training camp, he admits, he is haunted by the sight of tunnels by the runway, attesting to the desperation of those seeking an escape from the bombardment once night descended upon the capital.
"They were the tunnels of life. You confront reminders in every corner of the city, whether in bullet-holes in the walls or at military monuments. You are never far from the past."
Almost exactly 20 years on from the siege of Mostar, Bosnia are bound for their first World Cup. If Begovic and his brigade should need any appraising of the magnitude of that feat, their first match in anger comes against Lionel Messi's Argentina at the Maracana. The influx of the Argentinian disciples across the Brazilian border will be augmented by a vast delegation festooned in Bosnia's blue-and-gold. So enmeshed are this team in the nation's sense of cultural identity that the supporters are defined by their resolve to travel anywhere, at any cost.
Such a commitment exacted a tragic consequence when, after Bosnia's triumph over Slovakia last October to move within one win of reaching Brazil, three fans were killed in a road accident in the Polish town of Lomza. In a reflection of the extraordinary ties that bind this side, three players attended the funerals.
"I guess we also wanted to qualify in their memory," Begovic says.
For a population left scattered by war, soccer is a touchstone, a focal point for fierce patriotic energies challenged by the fraught transition to peace. Begovic, as a son of that mid-1990s diaspora, can empathise.
"It was always in the back of my mind to play for Bosnia, even though I was living in Edmonton and feeling a little removed," the Stoke goalkeeper says.
"I had represented Canada at youth level - only when I came to England was I put back in a Bosnian light. When the opportunity arose to wear the shirt, I didn't hesitate."
After an itinerant career that has taken him from Portsmouth to Yeovil, Ipswich, Macclesfield and La Louviere in Belgium, Begovic has found equilibrium at Stoke.
The 26-year-old has already had to resist overtures from Chelsea and Manchester United, in a rise that makes his father, Amir, dizzy with pride. Amir was goalkeeper for Yugoslav youth-level teams and Trebinje's FK Leotar.
Says Asmir: "In Bosnia I used to watch my dad train and play, and it seemed the natural route to take. I lived and breathed the idea of being a professional goalkeeper. It became my only goal in life. Everybody told me that I needed a backup plan through education, and while I made sure I had all of that, my first plan worked out."
Happily for his desire to reclaim his heritage through soccer, Begovic is part of an uncommonly gifted generation of Bosnian players. He is close friends with Manchester City's Edin Dzeko, and draws equal faith in his nation's World Cup prospects from the pedigree of Schalke's highly rated left-back Sead Kolasinac, dynamic Roma midfielder Miralem Pjanic, and Stuttgart forward Vedad Ibisevic.
"While we have finally broken that barrier of qualifying for a major tournament, we have known for some time that we have a strong crop of players," he says.
"It is the best Bosnia ever and we are making the most of it, so for that reason it doesn't altogether surprise that we're in Brazil. If we can keep producing brilliant youngsters we can continue to grow."
Under Safet Susic, the former Paris St-Germain and Yugoslavia striker and their coach since the team's inception five years ago, Bosnia had twice had brushes with the major stage before, reaching play-offs for the 2010 World Cup and Euro 2012 but losing to Portugal both times.
Once the Rubicon was finally crossed with that 1-0 victory in Kaunas, a wave of delirium was unleashed as tens of thousands of firework-wielding fans poured into Sarajevo's main square.
As Begovic puts it: "The joy was unimaginable - we knew the implications were humungous."
Even the speaker of the parliament broke off Bosnia's constant cross-party bickering to herald the team's return to a jubilant capital at 3am.
"The national team has shown us all how to achieve results, not just in sport but in any field," Denis Becirovic declared. "We can be successful if we work together. I hope this win sparks positive changes in our country."
Begovic, though, knows better than to be so blase when Bosnia is still blighted by economic stagnation and festering ethnic tensions.
"There are huge problems," he says. "A country that took such a battering for so many years has fallen behind the times, so it needs a lot of help to get back on its feet properly."
Begovic is determined that his own daughter, Taylor, should be steeped in the Bosnian way of life. Even 7200km away in Edmonton, his father would insist upon observance of Bosnian public holidays, and he is ready to impart the same philosophy.
"I try to speak a little bit of Bosnian with her at home - I probably need to do more," he says. "I take her to see the family in Bosnia. For her, being born and bred English, it's all very eye-opening.
"My wife, Nicole, was born in the US so we have different hymn sheets in the house."
He met Nicole on the south coast, when Portsmouth were sliding towards administration. Ever since, they have been an unlikely sporting combination as Nicole chases her aspiration to compete in equestrian dressage at the Rio Olympics in 2016. " Just like me, she is incredibly hard-working, and impatient," says Begovic. "It's crazy how sports can interact sometimes."
Soon both could be marking their mark in Brazil. For Begovic, who travelled yesterday to Bosnia's Sao Paulo training base to begin the final tune-ups, is convinced that even in a group containing Argentina, Nigeria and Iran, he and his teammates can exceed modest expectations.
"With our appreciation of the past, we recognise we have a duty as footballers to represent our country in the best possible way, to give the people something to cheer about and put smiles on their faces."
