City may have won the Capital One Cup earlier this month but their quadruple quest has ended with FA Cup and Champions League elimination - to Wigan and Barcelona respectively - in the past week.
In all competitions they have lost four of their last seven games, a clear loss of form after winning 18 and drawing twice in the previous 20.
Their sole focus for the remainder of the season is now their Barclays Premier League title challenge, but they face a difficult catch-up job.
City have slipped to fourth while concentrating on cup football over the past three weeks and are nine points behind leaders Chelsea, although with three games in hand.
Pellegrini said: "I hope that City will recover the performance that we played until one month ago.
"I think in the last month we felt a little bit the 18 games that we played in two months - that is the cost of being in all the competitions.
"I always want to stay in every competition, in the Champions League and FA Cup.
"But if you continue in it, it is more difficult. The amount of games in the last month has been very high.
"This is the only positive thing (from going out) - we can focus absolutely on the Premier League.
"That is why it is so important to win on Saturday because then we will have same as Liverpool and Arsenal, a week to prepare for every match."
Pellegrini admits he was caught by surprise by Wigan, who recorded another famous shock against City by winning at the Etihad Stadium in the FA Cup quarter-finals last weekend.
He views the midweek loss in Barcelona much differently, given that City had already been trailing 2-0 after the first leg, and takes encouragement from the display.
The Chilean said: "We need to work hard with everyone, with the staff, with all the players.
"We didn't expect to go out against Wigan. I think it is not normal but everyone tried as much as they can in every competition.
"Maybe we paid also for thinking about Barcelona three days after the cup.
"In the Champions League, it can be (defeat) when you play against Barcelona. You can win but you have a lot of chances to be eliminated because it is the best team in the world.
"Now we must try to fight for the title in the Premier League."
City are back in action at Hull on Saturday, with the 12.45pm kick-off meaning a quick turnaround after Wednesday's reverse in Barcelona.
Pellegrini feels his team must hit the ground running.
The 60-year-old said: "We need to win all the games from now until the end of the season.
"This game I think is special, it is more difficult, because we have less than 72 hours to recover and we are in a very difficult week after we were eliminated from both competitions.
"It is the moment to recover, to see our mentality and I hope we are going to do a very good game against Hull and get three points."
City will be without top scorer Sergio Aguero at the KC Stadium after the Argentinian felt a twinge in his hamstring at the Nou Camp.
He has undergone a scan but City are still waiting for results to assess the severity of the problem.
Pellegrini is hopeful Aguero, who missed five games with a hamstring injury in February, will be back within a fortnight - although a two-week absence would see him miss the March 25 derby against Manchester United.
He said: "I really don't know, but I don't think it is really very serious.
"I am hopeful he will (only) be injured for a couple of weeks."