The Belgian skipper looked shaky in defeat at Liverpool last weekend after a similarly uncertain show against Barcelona in the UEFA Champions League.
Martin Demichelis and Eliaquim Mangala comfortably shut out the Premier League's bottom club as goals from David Silva and James Milner kept the champions hanging to the coattails of leaders Chelsea.
Pablo Zabaleta also dropped to the bench, while Samir Nasri was excluded from the matchday squad altogether.
Pellegrini said Kompany the decision "without any problem" but refused to elaborate further on individuals who missed out.
"I thought it was important today to refresh the team both mentally and physically after we played two difficult games," the Chilean said.
"We didn't have the [results] that we wanted, so it was a good time to refresh the team.
"Whenever you do not get the results that you need, the next game is very difficult.
"That is why today the most important thing was to win the three points.
"It was important for our team to try and keep a clean sheet and dominate the game from the beginning."
