Pellegrini had Samir Nasri's late strike to thank for snatching a 2-2 draw against struggling Sunderland on Wednesday, a result that left City trailing leaders Liverpool F.C. by six points.
City have a game in hand on their title rivals, however, and the former Real Madrid boss is confident his side can overturn the deficit with five games remaining as the pressure increases on Liverpool F.C. and second-placed Chelsea.
"I am absolutely sure that the teams will drop more points also, it can be Liverpool F.C., Chelsea, the same way we drop points the last game," Pellegrini told reporters on Friday.
"We have to play another 15 points. We will try to win the most amount of points and at the end of the season we will see which team wins the title."
While Brendan Rodgers's Liverpool F.C. have hit a superb run of form at a crucial period, winning their 10 last league matches, City are limping towards the finish having won once in their last four games.
City's chances of reclaiming the title they won in 2012 have been hampered by injuries to crucial members of their squad and Pellegrini confirmed that midfielders David Silva (ankle), Jesus Navas (ankle) and Yaya Toure were unlikely to feature against West Brom.
"We continue with the same situation with Yaya Toure, David Silva and Jesus Navas. The three of them are injured at the moment," Pellegrini added.
"Yaya is improving but it is a muscle injury so it is difficult for him to be fit so soon."
Sixteenth-placed West Brom, who have 33 points from 33 matches, are unbeaten in their last three games and are slowly easing away from relegation danger.
Having drawn with bottom side Sunderland, Pellegrini knows his team must improve against West Brom especially given their style of play under coach Pepe Mel.
"I think that the performance in every game is very important and I hope we are going to improve our performance against West Brom," added the Chilean.
"He (Mel) is a manager that wants to play attractive football. His team try to have a lot of possession and have a very offensive game."