Matty Robson's second-minute header from eight yards looped past Joe Murphy and into the top right-hand corner to open the scoring, and although John Fleck, Franck Moussa and Leon Clarke all had good chances for Coventry, they failed to find an equaliser.
"It was extremely tough - the best 1-0 you will see," said Abbott. "It's fantastic to be involved in a game like that. We weren't very good at our job last week at Swindon, but we have beaten a strong Coventry side on a good run."
Abbott praised new signing Sean O'Hanlon, saying of the ex-Hibernian and MK Dons defender: "He played like a proper number five."
O'Hanlon and full-back Chris Chantler both had to receive stitches for head wounds and Abbott added: "I told the lads it was nice to see blood in the dressing room.
"Both players needed stitches. Chantler was sick the night before and wasn't going to play so he was magnificent."