"The ATP has adjusted its rule," Federer said. "Maybe the grand slams should adopt some of that. Maybe they should have a look at what they could do for the players to make it just a little bit easier.
"I feel for the crowd," Federer added. "They're there to watch good tennis, proper tennis. When I walked up, the chairman [Philip Brook] said, 'You guys should go and play for another set and a half'. I said, 'Yeah, let me go try to find Novak'. [But] it's unfortunate that it happened like this."
The prize money for first-round losers at Wimbledon is 35,000 ($62,000), a significant sum for all but the very elite. In order to collect the cheque, though, you have to begin your match.
The ATP's new rule allows a player to collect his prize money if he withdraws shortly before the event begins, thus allowing another player - a lucky loser from the qualifying event - to take his place. So far in 2017, the tour has seen more withdrawals (which happen before the match) and fewer retirements (which happen during the match).
"A player should not go on court if he knows he should not finish," Federer said. "The question is, did they truly believe they were going to finish? If they did, I think it's okay that they walk on court. Otherwise, I feel they should give up the spot."
Federer's victory means the Swiss has now moved ahead of Jimmy Connors with his 85th match win at Wimbledon - the most of the open era.
Earlier, Djokovic expressed his disappointment at having his opponent retire.
"It was great to be back on Centre Court. It's the cradle of the tennis history and it's a special feeling to walk on. It brings back many memories. It's nice to be back but you never like to end a match this way," Djokovic said. "He [Klizan] had issues walking on to court. I tried to focus on my game plan, I was serving well and when it mattered I made a break. But you could see he wasn't moving. I'm sure he didn't want to finish this way.
"It's Wimbledon and it's a big tournament. I wish him all the best."
Last year's finalist Milos Raonic joined Federer and Djokovic in the second round.
The Canadian sixth seed moved past big-hitting German Jan-Lennard Struff 7-6(5) 6-2 7-6(4).
Also through is last week's Eastbourne finalist Gael Monfils, the 15th-seeded Frenchman advancing in straight sets over German qualifier Daniel Brands 6-3 7-5 6-4.
However, his countryman Richard Gasquet was sent packing in a first-round upset to Spaniard David Ferrer. The 35-year-old Ferrer beat 22nd seed Gasquet 6-3 6-4 5-7 6-2.