City went ahead with goals from Yaya Toure and Vincent Kompany before Kieran Richardson pulled one back for Rene Meulensteen's men. Kompany then netted a bizarre own goal to level the Premier League clash.
Navas came off the bench to restore City's lead 12 minutes from time and fellow substitute Milner made sure of the points five minutes later.
"It was a hard victory," said City manager Pellegrini. "Fulham is not in a good position and they play an intensive game.
"Before they scored the first goal that was a counter-attack, we had at least three clear chances to score goals.
"The second goal was bad luck. It's impossible to repeat it, but these things happen in football.
"At 2-0 I think we were playing well. At 2-2 I thought we had to change something.
"The creative players were tired. We had other options, players with a different style of play, and I had to change something.
"Navas and Milner made a huge contribution to the team with two goals."
Asked for his opinion on Kompany's own goal, Pellegrini joked: "Maybe he didn't remember that we changed sides.
"After you win, maybe you can laugh, but he was not happy."
Joe Hart made his return to the City starting line-up at Craven Cottage and Pellegrini was positive about the England international goalkeeper's performance.
"I think he did well. It was not easy," he added. "The pitch was very quick and there was a lot of wind but I think Joe had a very good game.
"We don't know what happens in the future. We'll see what will happen. At the moment Joe will continue in the next game playing.
"As a manager I have to make the decision every week who will play, not just Joe Hart."
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