City looked jittery at times, having toiled on the road earlier this season in contrast to their magnificent home form, but wingers Navas and Milner turned the game back in their favour after Fulham came from 2-0 down to level the scores after the break.
"We were very nervous at 2-2 but Navas and Milner played very well and scored one goal each," Pellegrini told his club's website (www.mcfc.co.uk).
"At 2-0 we looked comfortable but at 2-2 I had to change something as we were not going to win the way we were playing.
"Some of the players were tired and some were not having a good day but with Navas and Milner we have another style of play and both were very important," added the Chilean whose side next host league leaders Liverpool on Thursday.
Yaya Toure's free kick after 23 minutes had put City in front before Vincent Kompany added a second but Fulham equalised through Kieran Richardson five minutes into the second half and when Kompany scored an own goal with an attempted clearance.
"Their second goal was very bad luck and it would be impossible to repeat," said Pellegrini. "But these things happen and the reaction of the team was very important."
Navas came off the bench to restore City's lead in the 78th minute and poor defending allowed Milner to wrap up the victory for the visitors in the 83rd.
"Fulham are a tough team at home and they defend very well," added Pellegrini. "We started well but after slipping back, Navas and Milner made huge contributions."
City, who moved on to 35 points and are above Arsenal on goal difference ahead of the north London side's home match with Chelsea on Monday, have now won four of their last five away games in all competitions but still do not look totally convincing on the road.