The reigning champions rediscovered their touch after four games without a win in the Barclays Premier League as they recorded a comfortable 4-1 victory at Stoke.
Sergio Aguero struck twice - his first goals in two months - while James Milner and Samir Nasri also found the net.
The result was not enough to cut into Chelsea's seven-point lead at the top - after the Londoners secured a last-gasp 1-0 win over Everton - but Pellegrini claimed that was not his first thought.
The Chilean said: "We needed this victory because in the last four games we didn't do it.
"Stoke are a tough team
I think we scored just one goal in the last three games against Stoke so to score four goals here is very important for the trust of the team.
"We will see if we can continue the same way in the future.
"We are not thinking about Chelsea
If they lose points it is good for us but the first thing for our team is to recover the sensation of (being) a good, solid team.
"That was the target and we did it."
City withstood a stern examination from Stoke in a compelling, end-to-end first half in which both sides had goals disallowed.
Peter Crouch cancelled out Aguero's opener with a fine header but both players were also denied by the referee.
Crouch was ruled offside after tucking in one rebound while Aguero was harshly penalised after the ball brushed his hand from a goalbound header.
But City upped the tempo after the break, restoring their lead with a Milner header.
Aguero's penalty after David Silva was fouled made victory certain while Nasri added a fourth with a fine strike.
Pellegrini said: "In the second half we continued pressing Stoke and didn't allow them to play in the way they like to with a lot of crosses.
"We finished by scoring three more goals and that is very important for the trust of our team."
Aguero's goals indicated a return to form in his sixth game since returning from a knee injury, although he was later withdrawn as a precaution due to a back problem.
Pellegrini said: "When Sergio has more minutes he will return to his normal level of performance.
"He felt something in the back
My feeling is it is not too serious and he now has 10 days to recover and train well
I hope he will be fit to face Newcastle."
Stoke boss Mark Hughes was pleased with how his side competed early on but accepted the visitors ultimately proved too strong.
Hughes, a former City boss, said: "I thought in the first half we played very well and arguably had been in the ascendency
We caused a very good team a lot of problems.
"I felt we had a clear penalty not given - they are the key moments against top sides you need to go for you.
"Unfortunately we didn't get that decision, which seems to be a recurrent theme at the moment.
"But second half, credit to City, they came out a lot sharper and put us under more pressure higher up the field.
"We are disappointed in terms of how we allowed them the second goal, but from that point we started to chase the game somewhat and that really plays into the hands of a team of City's quality.
"We were picked off and made errors as well
You can't afford to do that
We just weren't quite good enough to stop City taking the game away from us."
Source : PA
Source: PA