Mark Robins' side are back to winning ways after beating Port Vale 1-0 in SkyBet League Two.
Jodi Jones' first half curler gave Coventry the lead but the side had to work hard to defend their lead after Rod McDonald was shown a straigh red card with ten minutes to go.
"It was a tough game, and we made it tough for ourselves," said Robins.
"We created enough chances to see the game off. They set their stall up from minute one and they were just trying to pump the ball on top of our back four so it was just a case of us as a defence being brave enough to stay high, which we did.
"We did well to restrict them to chances until we went down to ten men and even then they did not have many.
"I thought that we were going to run away with it and the chances that went begging then become all the more important when we lost McDonald to a dubious red card.
"It may have been a foul, but it is the player who has caught Rod's feet so it did not really look like a sending off but we will have to see it before we appeal it. I felt it was a harsh red card.
The 1-0 victory means City earn their fourth clean sheet in six matches, the best defensive record in the division.
"A clean sheet is important and also it was a fantastic goal from Jodi. If you are looking for a little bit of brilliance you have found it there.
"The movment of Tony Andreu created a lot of that goal along with the other midfield players.
"It was great technique, and he found himself the time to move it from his right foot onto his left foot before finishing suberbly.
He added: "It was important that we built on the point we earned last week away at Chesterfield and this week to get all three, even though we have a couple of knocks and a red card but we can take those on the chin.
"This is a great result."