Sterling will play at Liverpool for the first time since his acrimonious £49million departure last summer as City travel to Merseyside on Wednesday.
The 21-year-old had a poor game when the sides met at the Etihad Stadium in November but performed much better against them - one bad miss in front of goal aside - in Sunday's Capital One Cup final at Wembley
In both matches he took stick from sections of Liverpool fans.
Pellegrini said: "I don't know which will be the starting XI on Wednesday but one player I am sure will start is Raheem Sterling.
"He's a young player - he's starting his career - and knows how to deal with the pressure
He will maybe receive the same treatment when he arrives at Anfield but I'm absolutely sure he can play without any problem.
"I don't have any doubt at all
It is important for him to play under pressure
I have 100 per cent trust in Raheem and I am sure he will be an important player in the game.
"In the way he played the other day, he demonstrated that he worked for 95 minutes, always concentrating on the game
He missed a goal but that can happen to any player.
"He was very difficult for (Nathaniel) Clyne in the one v one
I can understand after that game that he can play under pressure."
City prevailed on Sunday after extra time and penalties
Pellegrini expects both sets of players to be tired but hopes the joy of Wembley glory will put an extra spring in his side's step.
The Chilean said: "It was a very long game, but for both teams
I think both teams will arrive with the same hours of resting - but every time you win it is more easy to recover.
"I don't know how they (Liverpool) will react
It's the revenge, its another comp, they are at home, so we are sure it will be a difficult match to win but we will try to do it from the first minute."
City have breathed fresh life into their season in the past week with an impressive Champions League win at Dynamo Kiev as well as their cup final success.
Prior to that they had hit problems with back-to-back defeats to Leicester and Tottenham threatening to derail their title bid before a controversial FA Cup loss at Chelsea.
They now want to maintain the momentum and get their bid for a third league crown in five seasons back on track.
Pellegrini, whose side have slipped to fourth in the table, said: "It's very important we get the three points
If we have a successful game on Wednesday we are going to be going for the title in the end.
"We are not the favourites because we have played one game less and we are six points behind the leaders but in the Premier League, many things can happen."
When asked who he thought the favourites were, Pellegrini said at a press conference: "No favourites
When you have to play [for] so many points I don't think that one team can be favourites
It is difficult to know in this moment who will win."
Source : PA
Source: PA