The Sky Blues were 2-0 up thanks to goals from Leroy Sane and Sergio Aguero, but a header from Marlon Pack and a late goal from Aden Flint made the final minute nervy. However, an instant counter attack led to Kevin De Bruyne tapping home to ensure a 5-3 win on aggregate.
Guardiola expressed his joy when speaking to Sky Sports after the game, saying: "We're so happy to be there and for everyone involved at the club to reach this final. We played an amazing game until 2-0 and then we lost control, and in these kinds of games it's never easy until the end.
"But it will be a good lesson for us next Sunday in Cardiff and especially in the Champions League, in these kinds of situations to [play for] 90 minutes.
"In the first half we missed the last pass and we couldn't be more precise with more accuracy. We should have scored three or four goals and at 2-2 with a minute or two left anything could have happened."
The Spanish manager came under some harsh criticism for not winning anything in his first season in English football, but that looks nailed on to change this time around. However, he remained humble and insistent on the club's success rather than his own.
"It's not for me it's for Manchester City to try and reach another level. In the past [Roberto] Mancini and [Manuel] Pellegrini achieved that and we have to try and keep going for that level. The important thing for me is to be there and keep going in every game.
"We have a final against Cardiff and we're going to continue in the FA Cup and try to keep going in the Premier League as well."
Manchester City will play either Arsenal or Chelsea in the Carabao Cup final depending on the result in Wednesday's fixture.