The manager ripped into his players, accusing them of "jogging" through the opening 45 minutes, but his anger paid off as a Sergio Aguero hat-trick enabled City to reach the last-16.
"I wanted to change all of my players at half-time, all 11 of them," Pellegrini told a news conference.
"The whole team was a disaster in the first half. My team wants to win every game and wants to win the FA 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," Pellegrini added.
"If you don't play with 100 percent 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."
City have a 100 percent home record in the league this season, scoring 42 goals in 11 games and cracking 15 goals in their last three home matches.
Despite Pellegrini fielding a side packed with quality they were second best early on against a Watford side managed by former hospital janitor Beppe Sannino.
"The whole team didn't do the things that we normally do in the first half, the most important thing for me is Watford didn't score the third goal," said City's manager.
"If they'd have scored that the game would have been finished. But the reaction was there and we played a really good second half."
Despite averaging four goals in home games this season and suffering only one defeat at The Etihad, to Bayern Munich, City were frustrated for an hour against Watford who led through goals by Fernando Forestieri and Troy Deeney.
Aguero began the comeback when he tucked the ball in from close range and he curled in the equaliser after 79 minutes.
Aleksandar Kolarov's shot was fumbled in by Watford's keeper three minutes from time before Aguero took his tally this season to 25 and City's to 110 in all competitions.
"We didn't want him to play 90 minutes, the idea was for him to play 60 or 70 minutes but it didn't turn out like that," Pellegrini said of Aguero.
"We had to leave him on and he made the difference."