Former Watford and Birmingham striker Deeney was sacked on Thursday after just six games in charge of the League Two strugglers.
Things quickly turned sour for Deeney whose stinging criticism of his players, in particular Fankaty Dabo, raised eyebrows following last weekend's 2-0 loss at home to Harrogate.
The outburst was compounded yesterday by the EFL's decision to hand Deeney a four-match ban for his behaviour towards officials in the 2-1 defeat to Swindon on December 29.
Speaking exclusively to talKSPORT, Vince revealed Deeney's actions and subsequent suspension played a key part in the club's decision to part ways with him.
"I read some of what Troy said after that game, I didn't hear it," Vince told talkSPORT.
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"I thought it was wrong, very wrong. He did later apologise on Sky so I think he knows it was wrong.
"It was definitely a factor, that and our results. Not our performances so much because our performances apart from that game had been good.
"I hadn't had the chance to speak to him because I'd been busy this week and he also had a disciplinary this week with the FA. They banned him for four games for abusive and violent language towards officials.
"That was a new factor that that kind of thing [abusing officials] had happened. So really it was a bundle of things.
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"We haven't got a lot of time left to save our season and yesterday I felt it was better to make the decision sooner rather than later because I didn't think it was going to work given those things."
Despite a tumultuous week at the Gloucestershire club, Vince believes both Deeney and the club can take lessons from it and still hopes that the 35-year-old can go on to forge a successful coaching career.
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Vince added: "It was a less than ideal start from him in the world of being a head coach and for us as a club. I think it's something we can all put down to experience and there's plenty to learn from it.
"I hope that Troy learns from what's happened in the last week or so because I think he could go on and be a great coach, I hope so."