Sam Allardyce felt his battling Blues were hard done by as they exited the FA Cup - saying their performance at Anfield was at least worthy of earning a Goodison replay.
Everton were punished by what appeared to be a harsh penalty decision in the first half as Mason Holgate was adjudged to have fouled Adam Lallana, with James Milner converting the resultant spot-kick.
Gylfi Sigurdsson then capped a flowing counter-attack with a crisp low finish to level on 67 minutes, only for Liverpool debutant Virgil van Dijk to steal victory late on.
“I didn’t think [it was a penalty]. I think the referee made a mistake for their first goal and we made a mistake for their winner,” said Allardyce. “The rest of it, we’ve done brilliantly so I can’t ask for any more from the players in terms of their performance tonight and their desire to try to win the tie or at least take Liverpool back to Goodison.
“I’m very disappointed we’re not going back to Goodison and trying to get through to the next round.
“We may have saved it late on and I think it was a brilliant effort from the players, even though we’re disappointed.
“The performance deserved us to be able to take them back to our place, but that’s not to be.”
Everton confirmed the signing of Turkey international striker Cenk Tosun at half-time of the tie and Allardyce is hoping the 26-year-old can help give his side a greater offensive threat.
Sigurdsson, Dominic Calvert-Lewin and the fit-again Yannick Bolasie all had opportunities to add to the Blues' tally at Anfield, while substitute Ademola Lookman provided a lively cameo after replacing Wayne Rooney.
“What we’re doing I think is getting better from all angles,” he added. “But we need to be better in the final third - that’s what we’re trying to improve at the moment with the signing of Cenk, and we’ll keep working in that area so we can get more chances and score more goals.
“I am [pleased with his signing] because goals are a shortage for us. We really punished Liverpool on their corner with a breakaway goal tonight, which I was absolutely delighted about. But, yes, I’m pleased.
“I didn’t think there was any difference between the teams up to the final third and we’ve got to get better in that area, we’ve got to start delivering better quality to create more chances, become better finishers and score more goals. Then we’ll win more games.
“I think the midfield, the defence and the team defending tonight was very, very good.”