City came from 1-0 down to earn three priceless points in Group D thanks to two goals from the in-form Sergio Aguero.
City coped well with the much-criticised Khimki Arena pitch to boost their chances of reaching the knockout stages as they bounced back from the defeat to Bayern Munich last time out in the Champions League.
"I'm very happy. The result is very important for the team," said Pellegrini.
"The whole team concentrated with intensity on a difficult pitch."
Pellegrini also singled out Aguero and David Silva for special praise as they inspired City to their victory in Russia.
"Aguero and Silva are both top players and every match they show how they can play football," added Pellegrini.
"We are not in the next round but this is very important for us."
Manchester City midfielder Yaya Toure admitted the playing surface made it difficult to play good football and he also singled out Aguero as key to their success.
"The win was very important," said Toure. "It was very difficult to play good football. Full credit to the team, who worked very hard. It wasn't easy.
"Sergio Aguero had a fantastic game. He is an amazing player. Joe Hart saved us."