The Mexico forward had been hampered by a virus, but Pellegrini said: "He has recovered his shape now and I hope he will continue to score lots of goals for us".
"West Ham are good on the break, but we knew that", said manager Benitez.
Having looked in big trouble when they went 1-0 down at home to fellow strugglers Fulham towards the end of October, having lost their previous five on the trot, and having not won a game all season, Cardiff have started to show some real grit and determination.
West Ham's Javier Hernandez has scored 48 Premier League goals with all of those strikes coming from inside of the box - only Tim Cahill (56) has scored more goals in the competition with 100% of them coming from inside of the box. They have quality players, but in those circumstances you can't give them the kind of space we did.
Asked if that is the kind of quality he craves at St James' Park, Benitez replied: "Obviously it's a reminder that still we can improve things, and we have to improve things".
Southampton vs. Manchester United - Football Match Report
Sanchez is furious with Mourinho for dropping him for the champions league clash with Young Boys on Tuesday. Still seventh in the table, the Red Devils could end the weekend nine points off the top four.
"We felt confident beforehand, especially at home". In this his first Premier League season, Anderson is tied for first in team goals with Marko Arnautovic at 5, leads his team in passes with 587, third in shots with 19, and first in tackles with 37. He was risky on the break, finished with the highest passing accuracy of any West Ham player who started the game and was deserving of his late goal.
Perez endured a torrid time in front of goal during the first half, initially heading over from a corner when unmarked and then failing to hit the target with his left and right foot. So when he's at his best, he is a real player, very unsafe going forward.
Arnautovic could not complete the 90 minutes as Manchester City ran out 4-0 winners at the London Stadium but the Austria worldwide, who has scored five times in the Premier League this season, has been in training and will make the trip to the north-east on Saturday.
Hernandez, 30, has previously been linked with Newcastle.
"Momentum is always important and Newcastle have trust in this moment because they are winning", said Pellegrini.
"I have been very clear with the players that we have done nothing yet - we have to make sure we keep playing with the same intensity and attitude and mentality".