The Seahawks erased a 20-point fourth-quarter deficit to grab the lead with 31 seconds left but that proved just enough time for Atlanta to win it with a 49-yard kick from Matt Bryant.
"I can't imagine that anyone expected that we had a chance to get back in that game except for our guys in the locker room and they felt it the whole time," said Carroll, whose red-hot Seattle team carried a six-game winning streak into Atlanta.
"I don't know why they think that way but they do - and we got back in it and got ahead in great fashion."
Seattle quarterback Russell Wilson ended his unexpectedly excellent rookie season by throwing two touchdown passes and running in for another during a 385-yard passing performance but it was not enough to beat the top-seeded Falcons.
"There are a million things you can ask about it but all in all it was an extraordinary game an exquisite comeback," Carroll said after his team's 30-28 loss.
"The quarterback was incredible and everyone who made all those plays as we came back. We put ourselves in a position to be back for another game next week but we couldn't finish it with the couple of plays they made."
The Seahawks will regret a mix-up just before halftime when, well within field goal range and with no timeouts, Wilson was sacked on a third down and unable to get the next play off before time expired.
The missed three-point opportunity could have had an impact on the final stages but Carroll was not about to linger on that aspect of a poor first half display from the Seahawks.
"We had about five other opportunities to score," he said, before praising the way his team managed to grasp their way back into the contest.
"It's just an amazing football team we have. To hang like that, to be that tough, to finish like that, execute like that, it is just an amazing group, these guys have been pretty good for some time now but unfortunately we didn't get it done."
It has been a bright season for Seattle but no one has shined more than Wilson, whose confidence and all-round ability have won him many admirers.
"He is an amazing football player and he proved it again. He handled everything from the inside out ... it is so unheard of for a rookie to handle things like that, he just isn't a rookie. Look what he did today," said Carroll.
(Reporting by Simon Evans in Miami; Editing by Frank Pingue)