In-form City had struggled to get the better of the Magpies in the first period, but Danny Haynes was sent off just a few minutes before the break for a high tackle on Jordan Clarke and it changed the complexion of the game.
Just two minutes into the second half, Blair Adams crossed for Leon Clarke and he smashed the ball home via the underside of the crossbar and then doubled his tally after a mistake from Mark Fotheringham.
Hodge had led County to victory in his first game as temporary boss following the departure of Chris Kiwomya.
And the first 40 minutes had gone to plan against Coventry until the red card of Haynes.
Hodge said: "The first half was decent. We were coming up against an excellent team in Coventry and it was pretty even in that first half.
"But then things changed just before half-time. With 10 men it meant there were more spaces for their good players to use and we had a really bad start to the second half.
"One goal was our mistake and we know we can't keep doing that. You can't give presents away.
"There are some old pros in there who know the game. We went 4-4-1 and you have two banks of four and work hard and frustrate people.
"But once they got the first goal they relaxed a bit and then we gave them the second.
"All we do is come in Monday morning and start again - as everybody does. They players are down, understandably, but you learn to take the hits on the chin and move on."
- Sports & Recreation
- Danny Haynes
- Leon Clarke
- Jordan Clarke