The visitors had Conor Townsend sent off when the on-loan Hull defender collected two yellow cards in the space of as many minutes as half-time loomed.
Although the Millers had two efforts cleared off the line and Carlisle goalkeeper Ben Amos made a series of good saves, Evans' side just could not find a way past the Cumbrians' determined rear-guard action.
"Of course it's a opportunity missed," said Evans. "But every game we play when we don't get maximum points is an opportunity missed.
"It was a very frustrating afternoon for us. I have just had a look at the stats and we had 19 shots, but we lacked a bit of quality in the final third and we ended up taking pot shots from 30 or 40 yards - which is not us.
"I know we were unlucky once or twice but we need to be better in the final third than that. However, Carlisle gave their manager everything they've got.
"This is a very, very difficult league to win football matches in and the results show that. Our players covered every blade of grass but our decision making was a bit off, but you are going to have days like that.
"Our effort, commitment and passion was up there and that was plain to see, but we didn't play with any real zip in the final third and if you don't play with zip in the final third you are not going to create the chances. But having said that, we did create enough chances in the second half to win the game comfortably."