Heath's first game in temporary charge of the Sky Blues ended in a 3-2 defeat to Plymouth Argyle on Monday and City are now languishing in 16th place in the Championship and have gone seven league games without a win.
Several names, including Birmingham assistant manager and former Coventry boss Eric Black, have been linked with the manager's job at the City, but Heath insists he would love to keep the job.
He said: "I would love to keep this job.
People are very dispirited but we just need to pick ourselves up."
Heath also believes that he could not has asked anymore from his players during the defeat to Ian Holloway's side. He added: "I couldn't ask any more from the players.
It was just sloppy goals and individual errors which cost us again - as they have been doing in recent games.
"I thought that a lot of the players out there showed the desire to win, I can't fault them for their effort given the conditions of the pitch, which was not the best.
News RSS