Rocked by a third minute Stags goal by Krystian Pearce, the Imps had to wait until a 75th minute penalty equaliser from the spot by John Akinde to extend their unbeaten run to 15 games before the live Sky TV cameras.
“I was disappointed we started the game too passively,” he said.
“When we play that style we have to earn the right by the style and intensity of our play. We didn’t do that and conceded a terrible goal from a corner.
“We were away from home against a team with an excellent home record and a vociferous crowd, so you give yourself a mountain to climb.
“It knocked us and we didn’t play well for the first 25-30 minutes. We had to stick together in those moments to see that period through. Then I thought we did much better in the latter part of the first half.
“At half-time we reminded everyone of what has got us where we are and the qualities needed in the second half. So I was proud of the response shown.”
Cowley said he was disappointed his side did not play as well as they can in front of the live TV cameras.
“We do get some criticism for our style which we think is unfair,” he said.
“So I was disappointed we didn’t execute what I wanted technically and tactically, but we showed all of the mental qualities that have got us to this point.
“It was about their fight and willingness to never give up. If you refuse to lose, you will always stay in matches and give yourself an opportunity.
“It’s really hard to beat someone who refuses to give up and that’s what happened tonight.
“We could have folded in that first half hour as we’d come off script. That happens. They are human beings, not robots. It took us a lot to get everyone together tonight and I am really proud of the players.”