Rovers pulled off a textbook smash and grab raid to steal an important 1-0 win at the LNER Stadium.
“There would have been times where I would have been throwing people around the dressing room but I think I am beyond that now," said Appleton.
"There are a couple of things - one, I need those players on Saturday to go again and come again, which they will do and two, the reality is the performance was fine, it was okay, we didn't deserve to lose the game but we have lost the game.
"Hopefully, if we're clinical enough in the early part of the games, we're not having this conversation."
Lincoln had 71 per cent possession, more than twice as many goal attempts and Rovers’ one shot on target was Dan Gardner’s match-winning penalty.
Appleton said: “It was a good first half and we should have been at least three or four up but the inability to get that first goal and kill them off obviously cost us.
"I can be critical of the players and I have been between four walls and it'll stay that way but ultimately the opposition have been in our box once and we've lost the game so you have got to get the balance right.
"It still doesn't make me feel any better. It still makes me angry, it still makes me frustrated but the reality is that's what happened and we need to address that.
He added: “I'm disappointed and a little bit angry and frustrated - the players know that. These are the moments where sometimes in the dressing room you've got to keep your cool because all sorts of things could have gone off.
"When I watch the game back I think the dominance we had in the game will calm me down a bit and then, hopefully, come Thursday the players can clear their minds and get it out of their system because the games are coming far too quickly and far too fast to dwell on them for too long."