Kenny Dalglish's team halted a run of six years without a trophy at Wembley last month and Ayre believes this has redressed the focus on the club following a season marred by the Luis Suarez racisim row.
"We've had certain things that have gone on that people have put a negative slant on Liverpool, but this is a positive one and we should grasp it with both hands and move forward with it," Ayre told the club's official website.
"We've always said the way we perform on the pitch has a direct effect on the way we perform off the pitch, whether it's sponsors, community work or other things.
"We've shown we're ready to compete for trophies. We've won one and it means people see Liverpool are still up there and still a team competing for trophies. That's what we all need.
"On and off the pitch we need to be the best we can be. We're making great strides off the pitch, and now making great strides on the pitch.
"As long as those two things come together in tandem then the club has a great future."
Though Ayre condemned Suarez following the Uruguayan's decision not to shake Patrice Evra's hand, the board member was keen to ensure concentration remained on the team's success and looking further forward, avoided any more controversy.
"I think people probably underestimated at the time the significance of that win to us as a football club," Ayre continued.
"We've been through a lot in the last few years - our fans have been through a lot, everybody concerned with the club has been through a lot.
"I think getting to our first new Wembley final had a lot of significance for lots of reasons other than just winning.
"We've always spoken about progress, so if you win one trophy, then progress is at least another one and then another - but nobody is getting carried away either."
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