Evans, whose side led up until that point courtesy of Joe Skarz's first-half goal, was left seething after 71 minutes when his skipper Craig Morgan received a straight red card for his tackle on Callum Wilson and Coventry captain Carl Baker equalised from the resulting spot-kick.
And with the Millers goalkeeper pushed up as they searched for an equaliser, Baker fired in Coventry's third goal from the halfway line in the 14th minute of added time.
Pressley, who was sent to the stands following his protests after Rotherham took the lead, said: "We spoke before the game about how difficult it was going to be. For us to deal with what they threw at us was remarkable. I was disappointed with us in the first half because I know we are better than that.
"It was outstanding in the second half because we played in our normal controlled manner. I thought for such a young team it was a great result. I asked the players for an inspirational performance and that is what I got.
"As for my own performance, I have to apologise. I got a bit caught up in the game."