A runners-up spot behind Manchester City secured the Reds' first appearance in Europe's elite club competition since 2009.
Performances over the last 12 months have shown Brendan Rodgers' side have the capability to compete with the best teams, particularly at Anfield, and Allen is looking forward to the prospect.
"I can't wait. It was something that as a young footballer you dream about," said Allen.
"It is the reason you work hard every day, you strive to try to get there. I can't wait for the next season to kick off and experience one of the pinnacles.
"Obviously this season is just finishing but that is one of the big reasons to celebrate, we will be in the Champions League next season.
"As a player you set targets and goals and one of them is to play Champions League football. And I can't wait and I'm sure the fans feel the same way.
"Last year our record against the big sides was slightly disappointing, but this season we felt confident we could go into any game home or away and win and that's one of the biggest differences this year.
"That is a big marker for how far we have moved as a club. From an attacking point of view the amount of goals we have scored (101 in the league) is incredible.
"The record we have here at Anfield this season will play a big part as well. We look forward to next year and whether it be in the league, Champions League or the cup matches it is going to be a difficult place for teams to come, no doubt about that."
Liverpool missed out on a first league title for 24 years by two points and their destiny was in their own hands until the end of April when they lost at home to Chelsea.
Allen has warned his team-mates against complacency next season and is confident the hurt from missing out this year will act as a spur to go one better next term.
"Nobody would have predicted how far we have come this year. There is a slight disappointment in coming so close and not getting there but we still have a lot to celebrate," added Allen.
"I think it shows the belief we have got now. We'd have snapped people's hands off if we had have been offered it before the season, but it has progressed over the year and we realised how good we are as a team and how good the players we have as well.
"We can't become complacent because that is the danger, we will use this to spur us on next season.
"We always felt this season would be an important season to show the ability we have got as a team.
"It's great to have a club like Liverpool back at the top. The beauty of it is there is more to come. That is a great position to be in.
"The players we have got in this team would have experienced so much this season and it will be great going into the next few seasons for the club."