Liverpool put three past the Canaries at Carrow Road to advance to the fourth round of the competition and eliminate Norwich.
“It's a difficult one to take," Gilmour said. “We wanted to do well in this competition but we can't dwell on this now. We'll look ahead to the weekend against Everton."
City had a good chance to get back into the game at 1-0 down when Dimitris Giannoulis won a penalty late in the first-half, but Christos Tzolis was unable to convert.
“I back Christos to score all the time and that's the one time he didn't," Gilmour said. “We were attacking a lot, getting some good chances in that moment and then it put a real downer on it.
“If we scored that, it definitely could have been a different game. We had opportunities in the second half also to put away but it just wasn't to be.
“They're a top team and when we get an opportunity to score we need to take it. We need to be clinical and that's summed up our season so far. We're not scoring enough goals.
“All round, we need to put more pressure on ourselves to do well. We can't be giving away cheap goals, that goes for the full team. We're working on that so we can be more compact.
“We're hoping that we will click together because all the boys want to do well in the league and stay here, so hopefully it will happen soon."
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