Anthony Stokes gave Celtic an eighth-minute lead as the home side chased a 16th consecutive domestic win but Aberdeen came back strongly after the 20-minute mark and Russell Anderson and Peter Pawlett struck either side of half-time.
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."