A 2-1 victory over struggling Sunderland, the Reds' seventh successive win, highlighted how their remaining seven matches will not be plain sailing.
And while the focus is on the visits to Anfield of leaders Chelsea and Manchester City, Allen stressed Brendan Rodgers' second-placed side could not afford to be complacent against any team as a further seven wins are required if they are to stand any chance of lifting the title.
"There will be talk about those games (Chelsea and City) but there are three points up for grabs in every game, and every team we play are likely to have a lot to play for," the Wales midfielder said ahead of Tottenham's visit on Sunday.
"We are excited to be where we are, we are working really hard and are hungry to keep this run we are on going, but we have tough games from now until the end of the season so we have to keep fighting till the end.
"Until the very end anything is possible so we have to keep our focus and keep a strong mentality.
"Games like the one against Sunderland make us realise we can't be complacent for a second.
"Every team in this league is capable of hurting you and until the very death against Sunderland there was no moment when we felt we had the game completely wrapped up.
"We are our own worst critics and we will look at the performance and see where we can do better.
"We showed we were able to scrap it out, which is a strong ability to have."
Allen has started the last three matches - having made just eight starts prior to that run this season - but admits he can never take his place for granted.
"It is always difficult to establish yourself at a club like Liverpool when the competition for places is so great," he added.
"That is a big part of our success this season, everyone has added something different to the team.
"This season we have moved on, we have shifted a lot of ground in terms of how the team works and the self-belief is there for everyone to see.
"Every time we step out on the field we have the confidence to win matches."