It was a less than vintage display by third-placed City who had plundered 42 goals in their previous 12 home league games.
"The most important thing was to get three more points," Pellegrini told Sky Sports television after Yaya Toure scored the only goal in the 70th minute. "Stoke defended very well with 10 players behind the ball.
"We didn't find the spaces but we had the patience. I think it was very important to keep a clean sheet and be concentrated for counter-attacks and set pieces."
The victory was a pleasing end to a difficult week for the Chilean and for City who are three points behind leaders Chelsea with a game in hand.
European soccer's ruling body UEFA charged Pellegrini with misconduct on Friday, three days after he said Swedish referee Jonas Eriksson was "not impartial" in City's 2-0 home defeat by Barcelona in the Champions League.
"We know all the matches from now to the end of the season will be very difficult with every team and we hope we can continue winning," said Pellegrini who is also chasing glory in the FA Cup and League Cup.
"It just depends on what we can do between now and the end of the season."
City's first step towards an unprecedented quadruple is the League Cup final against Sunderland on March 2.
Pellegrini was coy about the possibility of top scorer Sergio Aguero returning after a hamstring injury.
"Sergio will start working with the team on Tuesday. We will see during the week if he is fit to play in the final," said the City boss.
Another forward, Stevan Jovetic, was injured within seven minutes of coming on as a second-half substitute against Stoke.
"Stevan felt his hamstring so we will see what the doctor says," said Pellegrini.
(Reporting by Tom Hayward; editing by Tony Jimenez)
