City were one of the favourites to win the competition on their way to potentially completing the quadruple - FA Cup, EFL Cup, Premier League and Champions League - but Wigan rewrote the script.
City had to play the second half with just 10 men due to Fabian Delph's controversial sending-off on the stroke of half time.
After the final whistle, Guardiola told BBC Sport: "Congratulations for Wigan for the qualification. We did absolutely everything, we made a mistake and this kind of game is like a final. OK, we accept the defeat. Congratulations to the winner.
"It was like a final. They had one shot on target, I don't have regrets with the way we played, the performance, the heart. I judge my players on intentions and not results and the intentions were good. Wigan won, congratulations to them and now we rest to prepare for the EFL Cup final."
City can pick up the first piece of silverware of the season if they beat Arsenal in the EFL Cup final this weekend.