The Hammers dominated for 60 minutes but eventually lost 3-1 after a flurry of goals from Arsenal across nine minutes in the second-half.
And Pellegrini has admitted he does not know if he will remain at the club.
He told Sky Sports: "It is difficult to understand. We dominated the game for 60 minutes and then lost the game. We didn't score the important second goal.
"You must understand the boos (from the fans) because the last five games we played here we didn't win. If you don't win at home your fans cannot be happy.
"You cannot concede three goals in every game. Unfortunately for us we are doing the wrong things. We are not in our best moment but need to keep fighting.
"We must play 90 minutes instead of 60 minutes like we did today. We must be solid all game. It does not depend on me what happens (with his future)."