Scott Severin equalised for the Dons within seconds of the restart but Charlie Mulgrew was guilty of some slack play in the build-up to United's second scored by David Robertson.
Diamond made amends for his earlier error by bravely heading home to earn the Dons a point but Calderwood was critical of his team's defensive display.
"I thought we were in the ascendancy for most of the game but it seems to be that when we play against United we give them gifts," he said.
"We have worked so hard to get our goals but we gave stupid goals away at the other end.
"I thought we had eradicated those mistakes from when we had our bad start to the season but they have come back to haunt us once again."
However he applauded his side for twice coming back from a goal down and felt they may have even deserved to take all three points.
"We showed a lot of courage to come back against a good team," he said.
"I suppose everyone will think a draw was a fair result but I'm disappointed because I thought we dominated the play."
Craig Levein, the Dundee United manager, admitted he was pleased to come away from Pittodrie with a point despite twice being ahead in the match.
"The result is a little bit frustrating but I have to recognise that it is hard to get points here," he said.
"If you asked me at the start of the season would I settle for two draws at Pittodrie I would certainly take a point on each occasion."
The United boss was annoyed that his side conceded a goal so soon into the second half.
"Being a manager can be the most frustrating job in the world at times," he said.
"At half-time I told the players to make sure they were switched on right from the start. I wonder if my voice is working at times."
Levein added that he felt the Pittodrie pitch was not particularly conducive to good football.
"It was a close-fought match littered with errors and the pitch didn't help," he added.
"I felt the pitch contributed to what I thought was quite a scrappy match.
"It was incredible how many free-kicks we gave away today.
"It made the game quite exciting because we were having to defend so many set-pieces. But I thought we showed a lot of determination and effort today."