Liverpool manager Jurgen Klopp felt the better side lost after West Ham secured a last-gasp 2-1 extra-time win in the FA Cup fourth-round replay at Upton Park on Tuesday.
West Ham were on the back foot for significant periods of the first-half but hit the post through Joey O'Brien and Dimitri Payet before Michail Antonio opened the scoring on the stroke of the interval.
Philippe Coutinho, playing for the first time in a month following a hamstring problem and having also struck the upright during the opening 45 minutes, clipped a free-kick under the West Ham wall to level matters three minutes after the restart.
Both sides pushed for a winner, with visiting striker Christian Benteke the prime offender in terms of missed chances after the match moved into extra-time.
In stoppage time, Lucas Leiva was adjudged to have fouled Enner Valencia and Liverpool's set-piece frailties came to the fore as Angelo Ogbonna leaped highest to convert Payet's pinpoint delivery.
"It's hard", said Klopp, who was back on the touchline following a bout of appendicitis.
"We were the better team, created chances and played good football, but we didn't use them.
"There were lots of decisions that on a better day I'd say were funny decisions. I don't think it was a free-kick [before Ogbonna's goal] but I'd have to see it again."
Speaking to BT Sport, Klopp added: "It's not easy because we were only here to win. You don't have to show your best, you just have to go to the next round.
"The door was wide open for us because we did well but it was not enough. We have to carry on and fight to the next game."