Brendan Rodgers' men are on a nine-match unbeaten streak in the league ahead of their trip to Southampton on Sunday.
Liverpool had only won two of seven games prior to that and there were serious doubts whether the Merseyside outfit could realistically challenge for a spot in the UEFA Champions League.
But Allen insisted there was never any concerns within the Liverpool dressing room.
"There was no doubt," said the Welsh midfielder. "We knew the level we'd been at previously and that we could get to it again.
"It was just a matter of how quickly we were going to get there.
"I remember being in the dressing room after that [Crystal] Palace game and I think that was the real low.
"Since then, we've shifted so much ground and taken so many steps forward, and we didn't doubt that we would get back to it.
"I think that is the main thing when you are in those situations. You look at the players you've got, the management, the support of the club.
"I think, with all those things combined, we always knew that we would pull through it.
"It was just about being patient, about sticking to our guns and working hard – all the classic cliches, if you like.
"Thankfully I think we are now reaping the rewards of that and we've still got enough time to push ourselves towards achieving something this year."
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