Sunday's 3-2 win over Norwich City saw the Reds confirm a top-three finish, marking a return to the competition for the first time since 2009, with a first Premier League crown now in the club's sights.
"It has always been tougher in the transfer market when you are not competing at the highest level," Ayre is quoted as saying by the Daily Mail. "We had the issue with Luis [Suarez] last summer because he wanted to play in the best games against the best players.
"That is always a factor. We have always been fortunate to be able to bring great players here despite that but there is no question [the Champions League] opens up a few doors for us and makes it a little bit easier.
"There is no question we always expected that the squad we need for next season will be very different to the squad that we have needed for this year when we were not playing in Europe."
Goals from Raheem Sterling and Luis Suarez held off a spirited display from relegation-threatened Norwich to see the club move five points clear at the top of the table and Ayre is delighted with the club's progress.
"What we achieved on Sunday was massive," said Ayre. "This isn’t just about getting in the qualifiers. We are guaranteed Champions League football. It is an unbelievable achievement from where we were.
"It is what we set out for but if you were taking bets at the start of the season, you would have said fourth place would be a great achievement. Now we are guaranteed third and we are determined to push on."