City recovered from 2-0 down to beat the Hornets 4-2 in their fourth-round tie at the Etihad Stadium thanks to a second-half Sergio Aguero hat-trick and a goalkeeping error.
Pellegrini said: "Yes, of course, I was very worried. If you don't play with 100 per cent concentration and intensity you don't win the game.
"I think Watford did in the first 45 minutes and we played jogging. That way it is impossible to win.
"If I could have changed 11 players at half-time I would have changed all of them.
"But it was more the thing of attitude and intensity than the performance of individual players.
"The whole team didn't do the things we normally do. The important thing was Watford didn't score the third goal. If they had scored the third goal the game was finished.
"Watford didn't surprise me. If you give professional players time and space they will make the difference.
"If we didn't make good pressing we were not going to have an easy game. That was what happened in the first half - and we were a disaster defending."
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