An own-goal from Aleks Kolarov put the Hornets ahead before two touches of brilliance from Yaya Toure and Sergio Aguero turned the result around in dramatic style.
The win leaves City just three points behind Premier League leaders Arsenal.
Pellegrini said: “We never give up, we have a lot of character. We won the Champions League group in the same way.
“We were unlucky to be losing. The corner [for Watford’s goal] wasn’t a corner and after that it was an own goal.
“But we continued trying to score, make substitutions and we were able to turn the score around.”
Pellegrini was praised for a tactical switch that saw Wilfried Bony replace Eliaquim Mangala with Brazilian midfielder Fernandinho dropping back into central defence.
The Chilean felt it was a natural choice to make, saying: “We were losing 1-0 so we had to take a risk. A draw was not good for our team. It’s not Fernandinho’s positon, but he’s an intelligent and tactical player and Watford were not going to attack too much.
“I think it was a close game and tough for both teams. They are in a good moment and playing well. But if you look at the statistics I think we deserved to win, we had more attempts, more shots on target, possession, but against I repeat a very good team.”
Toure scored City’s leveller for his third goal in four games - and it was another special effort from the Ivorian.
He darted towards the near post to flash a volley past the helpless Heurelho Gomes, but Pellegrini felt that was just reward for the pressure City had been applying.
“I don’t know if it was just a moment of magic,” reflected Pellegrini. “We had an important offensive volume, constant, and one of the good players with technical ability helped to decided the game.
“Before they scored the goal we also had clear chances with Fernandinho. But with Yaya, with Silva, with Kun, with Bony, with De Bruyne and with Navas we have technical players that can score and fortunately Yaya did.”
The victory was sealed when an excellent Bacary Sagna cross was met with a towering Aguero header - the Argentinian’s first goal since November 21.
“The goal is most important for a striker,” said Pellegrini. “Before the goal he made better movements than last game, so I hope next game we are going to see the complete Sergio.”
