The ex-Greenock Morton man came on with half an hour left and helped set up Anton Dowds’ header, but it was only a consolation effort, the damage already having been done.
The 25-year-old was brought on with Dowds and Leon McCann as coach Kenny Miller rung the changes.
Nesbitt said: “To be honest, at that stage, when we had just conceded the second, it felt really flat and horrible.
“It was one of the worst feelings I’ve had in football because we let the supporters down again.
“There was no pressure on us when we came on, so it was just about trying to make some sort of impact.
“I wanted to just come on and enjoy it because I haven’t enjoyed my football recently, to be honest.
“All three of us made a positive impact and the goal we scored was well worked, but scoring a consolation goal against Alloa at home shouldn’t be something to be happy about.”
Looking back on his side’s home results, he added that he feels something is clearly wrong within the squad to yield that sort of form.
“It’s been disgraceful,” he said. “The feeling of deja vu set in because we nearly scored a goal then conceded one straight away and it all fell apart. Today’s game was just like most of our home matches this season. It just isn’t good enough.
“Five home wins for any football club at any level isn’t good enough.
“Next season, that needs to change or the club won’t be back where they need to be.”
Nesbitt suspects that, like last year, a clearout is likely this summer, adding: “The club need to really rebuild and get into a much better position going into next season.
“It’s like a revolving door at this level of football and I am sure change will happen.
“Many players will leave and many players will join.
“I’m contracted to be here next season and there are eight or nine of us, I think, but we don’t know what will be happening yet.
“It will be like starting again because a season like this can never happen again.
“We’ve got one game left now and we need to at least go out on a win.”