Two-time Premier League winner Pellegrini endured an inconsistent debut campaign with the Hammers, finishing in tenth on the table.
And Zabaleta says the Chilean, who he won a title with at Manchester City, is trying to take the club higher up the ladder.
“I think we had a great season with a new manager in Manuel," he told beIN SPORTS.
“We didn't start quite well, as we lost the first four games of the season, [but we finished strongly with three wins and in tenth position].
“The Club really backed him with £80 million last summer and we need to give credit to the owners that they really gave him a chance to bring quality players into the team with the likes of Andriy Yarmolenko, Felipe Anderson and Issa Diop, so they made some great signings.
“With his experience, always working at top clubs, he is trying to take West Ham to another level."