Celtic manager Neil Lennon claimed his side deserved to win at Pittodrie on Tuesday night and blamed referee Craig Thomson for their first Scottish Premiership defeat of the season.
Lennon insisted Virgil van Dijk did not deserve to be sent off for bringing down Peter Pawlett in what Thomson deemed an obvious goalscoring opportunity and claimed Mark Reynolds should have been punished for a penalty-box handball.
Hayes said: "The first half I thought we were much the better team. I haven't seen Celtic being outplayed like that, even though they were down to 10 men.
"The second half we didn't control the game as well as we would have liked. We sat deeper and deeper and let Celtic back into the game.
"We were under the cosh for a while but I thought overall we just about deserved to win. We didn't feel we were going to concede a second goal at all."
Hayes ended Fraser Forster's 1,256-minute run without conceding a league goal when he found the top corner from 30 yards. The Irishman admitted it was a special strike but he played down their second win over Celtic this month, which came after Aberdeen lost at Partick Thistle on Saturday.
Hayes said: "It's probably my best strike. As soon as I hit it I knew it was going in.
"To be honest it was just like another game. We lost at the weekend and felt it was three points dropped. The manager told us to make it up by beating Celtic. That was more making up for losing on Saturday."