"It's similar to last season when we didn't start well and it was tough but we don't want that. We've seen good teams going down before so we must fight," Zabaleta told British media.
"We've got the quality in the team but the players need to put in good performances... you trust in the way he (Pellegrini) works because of the teams he's worked with before."
West Ham brought in former Manchester City and Real Madrid manager Pellegrini to replace David Moyes in May and Zabaleta said the new man needed more time to bed in his philosophy.
"For the first time maybe he doesn't have the same quality in the team like he had before. So maybe it'll take more time than at other clubs for him to get everything right," Zabaleta, who spent three years at City under Pellegrini, added.
"At Manchester City, there was so much quality, we won games easily. Here it's not the same. But he's a great man, a good manager and will try to find the best way to get the results."
West Ham travel to Everton after the international break, followed by home fixtures against Chelsea and Manchester United.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by John O'Brien)
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