Jurgen Klopp said the door had been "wide open" for Liverpool and hailed his young players' bravery after they exited the FA Cup as Angelo Ogbonna's 121st-minute goal sent West Ham through 2-1 victors.
The fourth-round replay at Upton Park looked to be heading for a penalty shootout at 1-1 deep in extra time, but Ogbonna headed home Dimitri Payet's free-kick to clinch a fifth-round tie away to Blackburn Rovers.
Earlier, Michail Antonio's opener for the Hammers on half-time was cancelled out three minutes after the break by Philippe Coutinho, who started for the visitors in his first appearance after a hamstring injury.
But despite forwards Daniel Sturridge and Divock Origi also returning as substitutes after lengthy absences, Liverpool could not find a winner.
"We played well -- the young players were brave," Klopp said. "It's hard. 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 [that led to the winning goal] but I'd have to see it again.
"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."
Among those who failed to capitalise for Liverpool was out-of-form striker Christian Benteke, who was clean through on goal in extra time only for West Ham goalkeeper Darren Randolph to deny him.
Asked if the Belgian needed a stroke of fortune after an 11-game goalless streak, Klopp said: "I don't believe in the easy goal. He has to carry on like this.
"It's not the nicest moment in his career but he has to work hard. He wants to score and we need him to score. We will work on it in the days, weeks and months."
"How can I say, it is not the most easy season for Liverpool FC."