Proud club president Ivan Vuksich said: "I think the team did fantastically to have got where they've got - it's just unbelievable."
The ASB Premiership club made history on Sunday when they beat North American champions Cruz Azul of Mexico on penalties to claim the third spot at Fifa's biggest club tournament.
Auckland were tipped out in their semifinal against South American champions San Lorenzo 2-1 in extra time, having held them to 1-1 in normal time.
There was also an individual honour for City captain Ivan Vicelich, who was awarded the bronze trophy for being third-best player at the tournament. Vicelich described the welcome as unbelievable. "It's been a long two days but it's great to be back home and seeing all the fans that have supported Auckland City."
He said their third place win was tough to get, but very special.
"We competed very well and we got a great reward for our win."
Winning the "bronze ball" for the third best player on top of the team's win was surreal, Vicelich said.
"[I'm] a bit speechless - it was great to be standing up there with some superstars, but the only reason that I've got it is because the team's done well, every player had to play good in every game and we had to make changes, the guys who came in played well, the staff worked really hard, the club's worked really hard."
Vicelich said he was looking forward to spending Christmas with his family at home, "it's a lot better than FaceTime or Skype".
And despite concerns the team would have to spend up to $50,000 on flights to get home by Christmas because their success meant rescheduling travel, all the players got new bookings. "Emirates have really come to the party," Vuksich said.
"They've managed to fit us in on about five or six different flights." The extra cost was less than $10,000.
Vuksich said he was incredibly proud of the team's successes. "I've run out of superlatives, to be honest. It's just put us on another planet.
"They're a wonderful bunch of boys, they're well-led, they've got a great staff and management team with them - we're very fortunate, a lot of good things have come together."