With the Spireites leading 1-0 thanks to Akwasi Asante’s 18th-minute opener, debutant goalkeeper Covolan, on loan from Port Vale, was shown a straight red card for an off-the-ball incident after initially rushing off his line.
With no substitute goalkeeper on the bench, midfielder Banks had to play more than 60 minutes in net.
Despite the circumstances, Armando Dobra doubled Town’s lead before half-time.
But the Blues’ 10-men could not hold and conceded twice from crosses before Branden Horton was shown a second yellow card for ‘time-wasting.’
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Cook had strong words for Covolan after the game, but had more sympathy for Horton, claiming referee Wayne Cartmel’s decision was a ‘joke.’
“Discipline, for any team to be successful, is paramount and today we have let ourselves down with our discipline and we will deal with it, it is as simple as that,” Cook said.
"If Lucas has made a decision it is probably a decision which has probably cost us a win.
"It is something that Lucas will learn from quickly, if he doesn’t learn quickly he won’t be at the club, it is that simple.
"We have to come away from home and be able to trust our players, it doesn’t mean that they play well, but we trust them.”
He added: “But I have got to go on record and say the Branden’s (Horton) second yellow is one of the biggest jokes I have seen in football.
"The game is over, the time is up, Branden is not involved in the incident, Laurence Maguire has hold of the ball, he rolls it down the line to me, I put my foot on it and he gives Branden a second yellow card and a red.
"A little bit of criticism is that the league has decided to appoint someone who has never refereed at this level before for a game of this magnitude today, which was always going to be a spicy game, so surely we should have had an experienced referee.
"Fair play to the referee, I have had a chat with him after the game. We had a very amicable chat. I just didn’t get Branden’s sending-off, I just don’t get how he can give a decision like that with the game over to a lad who is not involved in an incident. So the referees have got to learn, I am all for them learning, and we lick our wounds and go away.”
On the game overall, Cook said it was ‘action-packed’ and he was happy with the goals they scored but was disappointed to concede from two crosses.
He explained: "Unfortunately today, down to 10-men and 2-0 up, I always felt we could probably hang on, but it was going to be about defending a lot of balls into our box.
"Unfortunately, Ollie has made a decision to come for one and if he had stayed we might have seen it out, but there is no criticism of Ollie in any way shape or form.
"We are disappointed that we have only got a point but it is a point towards where you want to go.”
Cook also admitted the sending-off of Covolan ‘caught us out.’
He said: “We made the decision to go without a goalkeeper on the bench, it is something the club has done since I have come here. It is probably something I have never done as a manager.
"You can’t say it has bit us because would we have conceded with a goalkeeper in? Who knows.
"Dorking came on very strong in the second-half and probably deserved something out of the game.”
In terms of injuries, Cook added: "There are one two niggles around the club, Kabongo Tshimanga is back training flat-out but he has four minutes of football and I didn’t want to risk him on this pitch. He has not had any minutes yet but he is fit and raring to go.
"George Cooper has had a little bit of swelling on his knee that has gone down.
"Calvin Miller has a little bit of swelling on his knee that has gone down as well.
"Mike Jones has been sick for two days but he will be back on Monday.”