With one of the biggest games in the club's history to come on Tuesday, City could have been forgiven for taking their eye off the ball in the league.
But they could not afford another slip-up after the midweek draw with Newcastle and the 4-0 victory at the Etihad Stadium moved them closer to securing a top-four spot.
Manager Pellegrini said: "It was very important to have our mind focused on this game and not on Tuesday
"We did exactly the same before (the Champions League quarter-final against) PSG, we played a good game against Bournemouth
That is the best way
I always say a big team must be able to have their minds in both competitions."
City dominated the opening stages without really threatening until Fernando headed in Jesus Navas' corner in the 35th minute
Eight minutes later Sergio Aguero netted the second from the penalty spot after Ryan Shawcross had pulled back Kelechi Iheanacho
The Nigerian teenager took centre stage after the break, scoring in the 64th and 74th minutes on his fourth Premier League start
Pellegrini made several changes to his side with Madrid in mind, resting Vincent Kompany, Fernandinho and Kevin De Bruyne
The only real moment of concern for the City boss came when Yaya Toure went down holding his thigh late in the game, and Pellegrini confirmed his fitness will need to be checked
The Chilean said: "We play eight games in 30 days so it's very important to have some rotations
Fernando has a little pain in his knee and I didn't want him to finish
Kun (Aguero) is playing all the games
I didn't want him to finish
"Fernando, I don't think he will have any problem
Yaya, maybe the doctor will see him tomorrow
He finished with a muscle injury.
"For Vincent, it was a risk to play two games in 72 hours
It was better for him not to take a risk
He is okay, he worked this morning."
Iheanacho once again seized his chance to impress, taking his tally of goals for the season to 11.
The 19-year-old was a late substitute against Paris St Germain, and Pellegrini did not rule him out of playing a part against Madrid.
"It was a very important contribution, not just for this game," said Pellegrini
"Kelechi will have an important role in this club in the next years
"He is not only a striker who scores goals in the box
He contributes in the way the team plays
He scores two goals, he wins a penalty
I am very pleased
He can be involved in every game."
Stoke have little to play for in terms of the league and face ending the season on a real low after conceding four goals for a third successive game
Injuries are also mounting up, with Ibrahim Afellay set to be on the sidelines until 2017 after rupturing a cruciate ligament in training on Friday while veteran goalkeeper Shay Given came off at half-time with a groin problem
Stoke boss Mark Hughes said: " We are disappointed with the performance and the scoreline
We conceded too readily
"We are struggling with the injuries we are having and players are playing with restriction in their play in terms of their physicality
"Three poor games, too many poor goals conceded, but we have had a decent enough season
"We have three games to come
It is up to us to ensure we finish in a decent enough manner
We will go again."
Source : PA
Source: PA