Kompany was dropped to the bench along with Pablo Zabaleta and Edin Dzeko, while Samir Nasri and Fernandinho missed out on the squad completely as City beat the Foxes 2-0 at the Etihad Stadium.
Central defender Kompany had come in for particularly heavy criticism after City's damaging losses to Barcelona and Liverpool in the past week and Pellegrini decided to act with the season threatening to unravel.
Asked to explain his selections, Pellegrini said: "For the same reason Pablo Zabaleta, Vincent Kompany, Fernandinho, Samir Nasri, Edin Dzeko - that were playing normally - I think it was important to refresh the team mentally and physically after two difficult games.
"We have the squad we want so it was a good moment to refresh the team."
Pellegrini added that Kompany, normally an inspirational presence in the side but in poor form of late, took the decision "very well, without any problems".
City, trailing Chelsea by five points in the Barclays Premier League having played a game more, were not at their fluent best against the Foxes.
But they got back to winning ways with goals late in each half from David Silva and substitute James Milner.
After a difficult few days, in which Pellegrini's future has been the subject of speculation, the result was a relief.
Pellegrini said: "I think always when you don't have the result you need the next game is very difficult
That is why the most important thing was to win the three points.
"We dominated the game and had a good possession of the ball.
"Maybe Leicester is at the bottom but if you see their results - they drew 2-2 against Liverpool and against Everton and were very unlucky not to draw against Arsenal."
City created a number of chances but were denied on several occasions by veteran goalkeeper Mark Schwarzer.
Yet they still lacked their usual spark and Leicester were aggrieved to have been denied penalties on three occasions while Riyad Mahrez hit the post.
Asked if his side should have had penalties, Foxes boss Nigel Pearson said: "Yes
Simple answer
Three throughout the game - (Andrej) Kramaric in both halves, the second one you could probably say was a bit more marginal but there was contact
The third one on the line is in the box."
Pearson would not get drawn into criticising referee Robert Madley, who also frustrated Leicester with some of his decisions in an FA Cup tie in January.
He said: "I am not talking about them (referees), sorry
Not tonight
You can talk about them and ask the relevant authorities
I don't think there is any point me talking about the referee
Same one we had against Tottenham."
The result left Leicester bottom of the table but Pearson has no doubts about the spirit in his squad.
He said: "They are a resilient group so we will have to get on with it
We can't do anything about it
It is up to the authorities
Our players give everything they have got and they have done again tonight.
"There are lots of positive and we have to take them into the remaining games
There is no point dwelling on negative aspects of situations that we have no control of."
Source : PA
Source: PA