Celtic completed a domestic treble after Tom Rogic scored a stoppage-time winner in a 2-1 win at Hampden Park.
"We asked for that near-perfect performance and thought there was more to come from us," said manager McInnes.
"But we ran out of legs. It is our 351st day today since we reported back for pre-season."
That was because they were in the Europa League qualifiers after finishing runners-up to Celtic last season in the Scottish Premiership.
It was the same story in the league this season and Aberdeen also lost the League Cup final to Brendan Rodgers' side.
"It was fiercely fought and the performance was what I expected and what I was looking for," said McInnes. "But we came here to win, so obviously there's real disappointment.
"When it goes into injury time, a goal against you is always a sore one to take, but when it's a cup final, it just compounds it even more.
"It was like two proper heavyweights scrapping and fighting each other and everybody trying to find answers."
Aberdeen went ahead through Jonny Hayes after nine minutes, but Stuart Armstrong equalised two minutes later before Celtic completed their sixth win over the Dons this season.
"It was a huge effort from everyone and a real confident display from us for large spells of the game," said McInnes, who lamented a stray pass in front of goal from Hayes to Kenny McLean.
"We had moments in the game when we could have got ourselves in front again.
"It is all about those big moments. Kenny's got a chance. If he stands still, maybe it goes in, but it's just been a misunderstanding between the two of them.
"We implemented how we wanted to go about our business and get after them and Celtic struggled to get any real flow or rhythm into their game and that was important.
"We've done that in our previous two league games against them and we've had good spells in the game, something similar to today."
Rogic proved a thorn in Aberdeen's side again, with his fourth goal against the Dons this season.
"Celtic have got class players that can constantly ask the question of you," admitted McInnes.
"Rogic shows a bit of class. You've got to applaud and commend that level of skill, but we're disappointed we haven't won the cup because we wanted to win it for so many people."
Derek McInnes says his beaten Aberdeen players gave him the "near-perfect" Scottish Cup final performance he asked for but paid for an extra-long season.