Manuel Pellegrini and Vincent Kompany hailed Manchester City's never-say-die attitude after a 2-0 victory at Crystal Palace reinstated them as favourites for the Premier League title.

City's convincing win in south London means three victories in their remaining matches this season, starting at Everton on Saturday, would propel them above Liverpool in the table, barring a miraculous swing in goal difference.

Pellegrini's players watched Liverpool's defeat to Chelsea earlier in the day before securing a crucial three points at Palace, City's manager admitting that the result from Anfield provoked a reaction within the squad. The Chilean admitted that the title race was far from over, but praised his side's attitude following the defeat at Liverpool earlier in the month that appeared to have put a second Premier League triumph in three seasons beyond reach.

"We always trust we can do it," said Pellegrini. "After we lost to Liverpool I said we had to play three or four games more, each team, and in football all things can happen. We just had to win our games.

"We'll see if we cope [with the pressure]. We must win the three games. I repeat: I've always said that all big teams must be under pressure to win the title. They knew the score [at Anfield] and reacted in the best way: they knew if they beat Palace they had it in their hands. Now we must just think what we can do. It does not depend on other results. It's very important to play a good game against Everton and then the last two games."

Sergio Agüero tweeted: "Never surrender. Keep believing. Everything is possible so we must keep at it. C'mon, City!" while Kompany, the City captain, added: "It's in our own hands and you can't do more than that. There have been so many swaps and changes over the season, we are still very calm. We did what we had to do. It is difficult to predict the outcome of this league. You would be crazy to think it is over, but obviously we did our job. We are the team in the league that can't ever give up – especially after the year we won it."

City remain third in the Premier League, one point behind Chelsea and three behind Liverpool. However, the 2012 champions have a game in hand over their title rivals and a superior goal difference over both sides – 15 more than Chelsea and eight more than Liverpool.

Their trip to Goodison Park at the weekend could be yet another defining moment of a frantic season, before home matches against struggling Aston Villa and West Ham United. Liverpool play at Palace while Chelsea are home to Norwich.

Pellegrini praised the performance of Yaya Touré on his return from injury, the midfielder creating City's first for Edin Dzeko before scoring the second, and claimed that Liverpool were never likely to go on a 14-match winning streak until the end of the season.

"I don't know what happened with Liverpool because I didn't see the game, but the game we lost to them we didn't deserve to lose," said Pellegrini. "We played very well and had chances before Liverpool scored the third goal. It's very difficult for a team like Liverpool to win 14 games in a row. They had to lose one game, and this was the game.

"In the last game anything can happen. It depends on what we can do in the future. For now, we continue in third position. Liverpool have three points more, Chelsea one more. But we have to win. If we do that, we will see."