A weakened Hammers side were thrashed 5-0 by Sky Bet Championship side Nottingham Forest on Sunday, increasing the pressure on Allardyce.
West Ham are 19th in the Barclays Premier League having not won in that competition since November but Pellegrini is reading little into that form ahead of their midweek meeting.
Allardyce's side are at the Etihad Stadium for the first leg of their Capital One Cup semi-final on Wednesday.
Pellegrini said: "They had an awful result but I don't think they played with their best XI. They played with young players.
"I am absolutely sure tomorrow will be a very different game to what they played on Sunday.
"I think that in this job as a manager - in any club, in every part of the world - you are always under a lot of pressure.
"When the results are not the results the club wants, maybe sometimes it can be more nervous, but I think he is doing very good work in West Ham so I don't think he will have any problems."
Nevertheless, City, with their formidable home record, will be expected to win comfortably and take a big stride towards a place in the final.
That would put City, and Pellegrini, in clear sight of a first trophy since he took over.
With City also in contention in the Premier League and still in the Champions League and FA Cup the season has much potential, but Pellegrini is not looking too far ahead.
He said: "We are not thinking about the four trophies. We are just thinking about winning the next game we have to play.
"Tomorrow is one of the two games of the semi-final of Capital One, it is very important and we play here at home.
"We are going to have to have a very good performance to try to win against West Ham.
"After West Ham, we will think only about Newcastle. We are not thinking about the trophies, only the present."
After some rampant displays at home in recent months - notably scoring seven against Tottenham and six against Arsenal - Pellegrini knows how important another strong display could be.
He said: "It is very important to play the first leg here at home.
"Tomorrow we will try to win and if we can score more than one goal at home it will be very important also for the second leg."
Pellegrini is planning to make changes following the 1-1 draw at Blackburn in the FA Cup third round last weekend but was not specific at his pre-match press conference.
He did confirm that winger Jesus Navas would not be risked due to a minor knee issue and that Sergio Aguero, Stevan Jovetic and Jack Rodwell remain sidelined. Defender Dedryck Boyata is suspended after his sending off at Ewood Park.
Pellegrini has not decided which goalkeeper will play having rotated between Joe Hart and Costel Pantilimon since early November.
Hart is now re-established as first choice after his recent spell out with Pantilimon apparently reverting to domestic cup duties.
But the Romanian was at fault for Blackburn's equaliser as he returned to the side on Saturday and may not keep his place.
Pellegrini said: "I don't know exactly how many changes but we will make some.
"Tomorrow we will see the 11 that start.
"I think he (Pantilimon) has responded well. I analysed the performance with the players and tomorrow we will see which goalkeeper will start."
Pellegrini again insisted that, as yet, he has no plans to move into the transfer market this month and would not comment on speculation players could leave.
He said: "For the moment, (there is) no news.
"Of course if we bring a new player here to City it is because he is a very good player.
"In this squad we have a high level, so if we want to improve we must try to buy an important player.
"It is not our first concern and we are not in a hurry to make a decision. We are just seeing two or three things but nothing important."
Pellegrini dismissed a comment from midfielder Abdisalam Ibrahim about lack of opportunities at the club for young players.
Ibrahim, 22, who has failed to force his way into the first team in more than five years at the club, has claimed youngsters at City have little chance of breaking through.
But Pellegrini said: "I respect the opinions of everyone and I think good players will always have the chance to play everywhere."