Pellegrini’s side earned a 1-1 draw with the league leaders and were unlucky not to win the game.
Sadio Mane put Liverpool ahead before Michail Antonio struck an equaliser six minutes later.
And from there West Ham had the better efforts to win the game as Liverpool dropped points again.
They have won just twice in the Premier League since the turn of the year, losing to Manchester City and drawing with Leicester and West Ham.
And City will go top tomorrow night if they beat Everton.
Pellegrini was unhappy with the officiating but TV footage showed that Jame Milner was offside when played in before setting up Mane for the opening.
And Pellegrini snapped back when asked about Klopp’s comments after the match.
Pellegrini said: “Klopp is used to winning goals offside. He beat me against Malaga with Borussia Dortmund with a goal seven metres offside so he cannot complain about nothing.
“They have the two clear chances offside and they score one goal, so as I said last week we attack and defend very bad, tonight we did all very well and I think we deserve to win so that is why I am not happy with a point.
“I said in the press conference before the game that every game is different, you must play and it doesn’t matter if you play against the league leaders at this moment, the best defence in the Premier League and with an attack that scores a lot of goals.
“But if you create four clear chances and you didn’t score and they have two clear options – one that they score a metre and a half offside, and the other with Origi in the last minute in front of the linesman is again offside.”
Klopp had moaned about the officials and ranted at referee Kevin Friend at full-time.
Klopp told Sky Sports: “We had good moments, coming through the channels and scored the goal, which I’ve now been told is offside. This explains a little bit the second half, because I think the referee knew at half-time.
“He knew it for sure at half-time, and then you saw a lot of strange situations. They were not decisive but just rhythm breakers. That obviously didn’t help us.
“If I’ve made a mistake in the first half, I don’t want to open the gap even more as a human being.”