The Citizens were two goals down at half time, but scored four times in the second period to book their place in the fifth round of the cup.
"I was very worried at half-time because I talked with the players a lot before the match and said that in the FA Cup, teams that play in a lower division have a lot of motivation," he told reporters. "If you don't play with 100% intensity and desire you can lose and go out of the competition and we were jogging in the first-half - if you play like that you can't win.
"I didn't underestimate Watford, I didn't think it would be easy and I told the team this. The players must not believe they have an easy game but I feel that they had a very good reaction in the second half.
"We changed everything, we played with tempo, with pace. We continued playing in the same way we've played in this whole season at the Etihad. This reaction was very important."
City are next in action when they visit Tottenham Hotspur in the Premier League on Wednesday.