The final was level at half-time, but two quick headers from Nico O'Reilly early in the second half settled the contest and handed City their first trophy of the season.
Guardiola was full of praise for his players, especially given their recent struggles.
"We could not win against Nottingham Forest at home or West Ham away, and we lost heavily to Madrid," he said. "So honestly, not even I gave one pound for our chances today. But the players proved again what they are capable of.
"Second half, with and without the ball, we were unbelievably good. I could not believe the level we reached."
City had to survive early pressure, with goalkeeper James Trafford making a key save, but once they settled, Guardiola felt the control shifted.
"They suffocated us in the first 15 minutes," he said. "After that we started to win second balls and take control. Everyone contributed - that is what these competitions demand."
The manager also highlighted the impact of his younger players, singling out O'Reilly for special praise.
"Maybe he has been the signing of the season," Guardiola said. "He can play in many roles and he scored two fantastic goals today."
Guardiola's emotions spilled over on the touchline, sprinting in celebration after the goals.
"If I cannot celebrate like that, then when?" he said. "I am a human being. I have emotions and I express them."
For O'Reilly, it capped a perfect weekend after turning 21.
"An amazing day," he said. "We came out strong in the second half and dominated. Now we celebrate."
Arsenal manager Mikel Arteta defended his decision to start Kepa Arrizabalaga, who was at fault for the opening goal.
"I had to be fair," Arteta said. "He has played throughout the competition. We will use this disappointment as motivation for what is ahead."
Despite the win, Guardiola played down its impact on the Premier League title race, with City still trailing Arsenal by nine points, although they have a game in hand ahead of next month's crucial meeting between the sides.
Assistant coach Bruno Saltor has admitted Tottenham could not cope with the "weight" of the occasion after a damaging 3-0 defeat to Nottingham Forest on Sunday left the club hovering just above the relegation zone.
Mikel Arteta has called for "fire in the belly" but calm heads after Arsenal suffered a 2-0 defeat to Manchester City in the Carabao Cup final at Wembley Stadium on Sunday, ending their hopes of a historic quadruple.
Arsenal's quadruple hopes were put to an end with a 2-0 Carabao Cup defeat to Premier League title-rivals Manchester City.
Pep Guardiola has confirmed that James Trafford will start in goal for Manchester City in Sunday's Carabao Cup final against Arsenal.
