The Argentine has struggled to blend together Chelsea's expensively-assembled squad since taking over in the close season and his team are a lowly 11th in the Premier League.
Some fans even chanted the name of former manager Jose Mourinho during the 2-2 draw at London rivals Brentford.
Chelsea have managed one win from their last five league games and on Monday host Newcastle United as speculation over Pochettino's future continues to swirl.
"We need to try and improve in the way that we play," Pochettino told reporters on Thursday.
"Of course, we need our fans. We hope the fans will be behind us on Monday to help us win the game. That is so important for our players.
"We need to accept the frustration. Maybe if I was a fan I'd be the same because we are not matching the expectation. We must be responsible for our performance and try hard to improve."
Chelsea missed a host of chances in the League Cup final before losing 1-0 to Liverpool after extra time and on March 17th host Leicester City in the FA Cup quarter-finals. However, it is on their league position that Pochettino will be judged.
"We are suffering negativity but we can't stop believing, we must keep believing and try to perform on Monday," the Argentine said. "I really believe we can succeed.
"We analyse all the circumstances and here we are. We got to a final and we fully deserved after 90 minutes to win the game.
"We can believe that we can start to win games to get close to qualifying for Europe. The opportunity is there but if you give up belief we will go down (the league)."
Chelsea have injury problems ahead of Monday's clash with eighth-placed Newcastle.
Defenders Levi Colwill and Ben Chilwell are both doubtful while captain Connor Gallagher has missed training.
"Gallagher isn't training because he has a virus," Pochettino said.
"We'll see if he can train tomorrow or Saturday but the problem is you have to wait with this situation. We don't know what level he'll be at when he recovers. We'll have to assess him."