Celtic manager Neil Lennon admitted his side got what they deserved out of the game following a disjointed display.
"Defensively and midfield-wise we were second best," Lennon said.
"We started the game well and then our passing was just so poor. We never really had a concerted period of pressure to work the Aberdeen goalkeeper.
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"It's very difficult to single out any player with any credit - Stokes possibly and James (Forrest) maybe had a spark but the rest of the team were very flat.
"We prepared them so well and talked about set-pieces. We were really poor for the first goal, both centre-halves missed the header. And then we had an opportunity to clear and we duff it and got punished.
"That was symptomatic of our overall performance. We played like strangers at times and for relatively experienced players that's very disappointing. There was a lack of real hunger and dynamism.
"But you have got to give credit to Aberdeen, they came here with a game plan and it worked out well for them."
Aberdeen manager Derek McInnes was proud of his players' confident attitude after they came from behind to knock holders Celtic out.
Aberdeen have suffered 17 consecutive league defeats at Celtic Park, although they won there in the Scottish Cup in 2008.
But McInnes sensed a confidence in his players all week after Aberdeen's 4-0 League Cup semi-final win over St Johnstone and was delighted to see them carry that on to the pitch.
"The performance is something I know we are capable of so I'm probably prouder of the mindset," McInnes said.
"When you are the underdog, it's normally about reinforcing confidence and getting belief in the team but we didn't have to work too hard at that this week.
"Last week was a good hurdle to come over and that reinforced the confidence. Going behind early was disappointing but the response was terrific.
"I know with the demands of Celtic and their standards, people will maybe look at Celtic's failings, but I think we restricted them. We never allowed the game to be stretched, we never allowed their better players to affect the game too much.
"I have been here as a manager and a player when you feel as if you are hanging in and I never felt that today. Even when it was 1-1, it was about what we can do to win the game. More importantly, the players believed they could go and win it, and that's brilliant to see."
Defender Mark Reynolds felt the victory was further evidence of the transformation of the team's mentality.
"Everybody was tipping this week to make or break the season," the former Motherwell centre-back said.
"I think a lot of people were hoping it would break the season but we came out the other side.
"I think it has shown there's a new Aberdeen, not the team that was there before where they started crumbling under that type of pressure."