Yaya Toure's 70th-minute goal proved to be enough to see off a stubborn Stoke side and maintain City's Premier League title challenge.
The home side were far from their best throughout the game and Pellegrini was just happy with the three points to stay in touch with leaders Chelsea.
"The important thing was to add three points more to the table because we know all the matches from now until the end of the season will be very difficult with every team, and we hope we can continue winning," Pellegrini told Sky Sports.
Asked if the midweek game against Barcelona played a part in City's lacklustre showing, Pellegrini added: "Maybe it had some relation with one match, another one, but I also think it was down to Stoke.
"They defend very well with 10 players behind the ball, we didn't find the space but we had the patience to try until the end.
"I think that is the way they must play here. For Stoke it is very important one point here, a draw, so I understand perfectly. But I think it was very important to keep our clean sheet and to concentrate on the counter-attack and set-pieces and also have patience to score."
The win keeps City within three points of Chelsea with a game in hand and Pellegrini insists they will try to win every game with their destiny in their own hands.
"We just depend on what we can do until the end of the season," added Pellegrini.
"We are three points from the top of the table but we have [played] one game less so it is important to always depend on what work you do."