Calderwood told Setanta Sports 1: "All credit to Rangers; I thought they played very well.
"They knocked it about, they caused us problems with their system, with Lee sitting in front of the back four and our passing was off.
"We looked tired for some reason so I was well pleased with the result to be honest."
"We actually said they may leave big Kris out. It's always a difficult game for them up here," said Calderwood, whose side survived a scare when Nacho Novo hit the post late on.
"They caused us problems all day to be honest. I thought we defended really well, got the luck when we needed it.
"I don't know if we deserved a draw but it could be a very important point come the end of the season."
"We could've nicked it in the end with Charlie," added Calderwood.
"But we didn't deserve any more than that."
Rangers boss Walter Smith felt his side did enough to win the game, saying, "I thought we played very well today. I felt after the opening five-10 minutes or so, when it's always a bit scrappy, we settled down and dictated the way the game was going to be played.
"I thought we were excellent.
"Aberdeen made a change in the way they played at half-time. Again, there was a 10-15 minute spell where it was quite even.
"I felt we dominated the latter stages of the match.
"I felt overall, with the amount of opportunities and possession we had, we deserved to win the game.
"The way Aberdeen were going, they're very direct in the manner they're playing now, winning the ball when it was dropping down was an important factor."