"I thought we were outstanding at times and could have scored a few more," said Rodgers to the Press Association.
"We are offensively minded and got punished. It was a sloppy moment for us which gave them hope.
"The game became a bit of a war after that. But we were well worthy of the win. Coventry have some good players and made us work hard.
"There are moments we can pick out to improve on. But we are learning our lessons which is important.
"We have a good home record and that's three wins in a row here. But we have to continue doing the right things without the ball as well as with it.
"It's about building on this by beating Scunthorpe on Saturday.