Jurgen Klopp refused to blame Loris Karius for West Ham's first goal in the 2-2 draw at Anfield after the keeper got a hand to Dimitri Payet's free kick but failed to keep it out.
Divock Origi's fourth goal in as many matches salvaged a point for Liverpool after Payet's goal and Michail Antonio's first non-headed strike of the season had turned things around following Adam Lallana's fifth-minute opener.
Despite the four goals, all the focus was on the goalkeepers as Karius and West Ham's Darren Randolph both made costly errors.
But Klopp felt bad luck, rather than any lack of endeavour, had prevented his side from winning.
"We tried everything,'' he said. "The [West Ham] goals -- one is a wonderful free-kick and one we were very unlucky -- they were a big surprise for everybody.
"We should have had more, we tried everything.
"It's a draw, we have to take it... it felt like we were the whole time in their box.
"We haven't made the right decisions, you need a little bit of luck. A draw doesn't feel too good but it doesn't feel too bad either. We are still a really good football-playing side.''
West Ham boss Slaven Bilic immediately turned his focus to Wednesday's game against Burnley, with fellow strugglers Hull and Swansea following in a crucial run of games for the Hammers.
"We have a couple of games we have to win that can get us into a more comfortable position,'' he said.
"It's going to be a difficult couple of games and we have to show our quality. We're going to be ready for Burnley on Wednesday.''