Mark Robins praised 10-man Coventry's resilience after they reached the EFL Cup second round with a 1-0 win at MK Dons.
Defender Declan Drysdale was shown a straight red card in the 27th minute for a foul on Matthew Sorinola, while Marko Marosi saved Carlton Morris' resulting penalty.
The Dons had the better chances but summer signing Tyler Walker fired in the winner eight minutes from time to secure a place in round two for the Championship club.
"Thankfully we took one of our chances. That's why we brought Tyler in, it's a great goal to register and to get us into the next round. We really wanted to get into the next round," Robins said.
"I'm happy with the result and the way we've applied ourselves because the sending-off was really harsh.
"You look at the double-jeopardy rule where you've got a sending-off and a penalty. I asked the referee the question and, basically, the answer that came back is that if it's an upper-body contact then the double-jeopardy rule goes out of the window. Now there was no upper-body contact, it was all legs at worst.
"Whether it was a penalty or not is debatable, but it certainly wasn't a sending off. That put us on the back foot. Against a side who clearly keep the ball really well and move the ball really well it meant we had to do a lot of running.
"We did – and we did it really well. We managed to get the best chances in the game other than the penalty, which was a fantastic save from our keeper and kept us in it."
Aside from his penalty save, Marosi also denied Morris from close range and tipped a header from the striker round the post.
Coventry's Ryan Giles went close with a shot that flew just wide in the first half, while Kyle McFadzean was denied by a smart save by Dons keeper Lee Nicholls after the break.
Coventry could have extended their lead but Amadou Bakayoko hit the post it the dying stages.
"I thought we'd go on and win, but we created chances and should have scored a couple of goals," said Dons manager Russell Martin.
"But we didn't and I said at half-time the only way they would score would be through a counter-attack or a set-piece.
"Unfortunately we didn't deal with the big moments and I'm angry with that. Their performance deserved a lot more and I don't want to see that again – and they don't want to see that again.
"I don't want to feel that way again where we play well and there are so many positives, but we end up losing 1-0."