Pellegrini dropped Hart for Saturday's Barclays Premier League defeat of Norwich and his replacement Costel Pantilimon will continue against CSKA Moscow in the Champions League this week.
The England goalkeeper has paid the price for a number of high-profile errors over the past year for both club and country.
This season alone he has made costly mistakes against Scotland, Aston Villa, Bayern Munich and - most recently - Chelsea.
With pressure growing, Pellegrini felt the time had come to make a change but he been impressed by the player's reaction.
Pellegrini said: "I think Joe has reacted very well. He is a professional player.
"For him it is also a good thing to have a rest after playing so many matches.
"He is working without any problem, supporting Costel Pantilimon.
"Nobody wants to be out but he thinks it will be useful for him."
Hart has been City's number one since being unexpectedly promoted ahead of Shay Given in 2010.
For most of that time he has been outstanding and it is only in the past 12 months that regular errors have crept into his game.
Pantilimon has had to wait patiently for an opportunity since being brought in as Hart's deputy in the summer of 2011, featuring only in domestic cup ties until Saturday.
The Romanian's belated Premier League debut proved rather uneventful from his point of view as City romped to a 7-0 win and were hardly tested defensively.
On that basis, Pellegrini will not be reversing his decision as City bid to claim a place in the Champions League last 16 at the expense of the Russians.
The Chilean said: "I don't know when Joe will come back to the team. It is very important for him to have a rest.
"He has played all the matches for two-and-a-half years.
"We will see in the future what we must do. For today, Pantilimon is playing."
Pellegrini's prime concern now is ensuring City reach the knockout stages of the Champions League for the first time.
After City's failures in the group stages in each of the past two seasons, progress this time is a minimum expectation and Pellegrini was appointed in the summer with his European record in mind.
The 60-year-old has taken Villarreal to the semi-finals and Malaga to the last eight of the competition in the past.
He said: "For Manchester City it would be a really great achievement.
"We all know what happened the last two years - they couldn't get to the round of 16.
"For a club that is trying to grow every day, to go to the next round is very important."
City will qualify if they repeat their victory over CSKA of a fortnight ago - they won 2-1 on a difficult surface in the Russian capital - and Bayern Munich avoid defeat against Viktoria Plzen in the other Group D game.
Pellegrini is focusing only on that objective and, with his side having been taught one footballing lesson by Bayern this term, not getting carried away with what might lie beyond.
He said: "We have a very good squad and the minimum thing this squad needs is to qualify for the round of 16.
"After that, in two-legged play-offs, anything can happen.
"We will try to do the first step and then to continue in February - but for the moment our only target is to qualify tomorrow.
"It is not easy to talk what can happen in the future."
City will be without striker Stevan Jovetic, who suffered a calf injury in last week's Capital One Cup win at Newcastle.
Captain Vincent Kompany also remains on the sidelines as he continues his recovery from a groin injury.
Pellegrini said: "Jovetic has at least three weeks (out). Except Vincent Kompany and Richard Wright, all the other players are fit."