Brendan Rodgers' first season in charge saw some progress made but the Reds still finished 12 points adrift of fourth place.
Bridging that gap, having improved one place and five points on predecessor Kenny Dalglish, will not be easy and will be more difficult if the club cannot hang on to striker Luis Suarez.
A good transfer window would help but there is still plenty of ground to make up before Liverpool can return to Europe's elite club competition for the first time since the 2009-10 campaign.
"If we can add quality to the group over the summer and improve on the things which let us down then that will stand us in good stead for next season," Ayre said.
"The expectation is keep progressing and of course our ambition is to play in the Champions League.
"This football club is steeped in the tradition of the European Cup. That's where everyone wants to be from the owners down.
"But there is no point saying we expect to finish in this position. All that does is just focus everybody - the world's media - on a particular place.
"We want to be playing in the top flight of European football. That's why fans buy tickets because they want to see Liverpool at that level.
"Our ambition is to get there. Whether we do that one year, two years or three, we will see. That's where Liverpool Football Club should be."