Liverpool manager Brendan Rodgers was unhappy with referee Howard Web for not giving a penalty when Alex Oxlade-Chamberlin fouled Luis Suarez late in the game.
Liverpool had already been awarded a penalty earlier when Lukas Podolski had brought down Suarez in the box, but the second appeal was waved away by the Rotherham ref.
Arsenal held on to a nail-biter to beat Liverpool 2-1 and will next face Everton at the Emirates in the quarter-finals.
When talking to Sky Sports after the Match the Liverpool boss said: “He’s always asking questions of defenders, and quite a lot of the time he doesn’t get what he deserves,” Rodgers said about Suarez.
“The one at Chelsea (when Samuel Eto’o fouled Suarez in December) was a clear penalty. He’s got a penalty but should’ve deservedly had two penalties today.
“And if it is a penalty he should have it, irrespective of what his reputation is.
“I thought that was quite an easy decision for the ref.
“We’re bitterly disappointed to have not got that because then it just keeps our momentum going for the final stages of the game.”
Rodgers did not talk to referee Howard Web after the game, but said he will be looking for an explanation as to why he did not give a penalty.
The Liverpool manager added: “For me, it’s gone. You can’t change it, you can’t affect it. I’ll speak to an assessor.
“It would be nice to know why it wasn’t given, because it can be a defining moment in the game.”
There was also a question mark as to why Liverpool captain Steven Gerrard was not sent off after a foul on Oxlade Chamberlin after having been already booked.
Rodgers added: “I think it was a foul. I’m not so sure it was a yellow card. Howard’s used his common sense. He got that correct.”
The game might have been different if Liverpool striker Daniel Sturridge could have put away two early chances but it was not to be after hitting the side netting with one and sending the other over the bar.
“He’s disappointed and he’ll be disappointed for the team as well,” Rodgers added.
“I thought our performance level was outstanding.
“To come here, virtually dominate most of the game and look a real threat going forward, to end up with nothing in the game disappoints because it was a competition we wanted to do well in.
“We could very easily have had another five or six goals today, but we weren’t as clinical.”
Liverpool have only one target left now this season and that is finishing in the top-four where they are currently just four points behind leaders Chelsea.
Rodgers added: “It narrows our focus now into one competition and we just continue with the confidence and the belief we’ve been playing with.
“We’re going to have a really exciting 12 games to finish.”