The Seasiders began the third-round tie in the Championship’s bottom three after a nine-game winless run, but stunned their Premier League opponents.
Marvin Ekpiteta gave Appleton’s side a slender interval lead and after soaking up second-half pressure they added further goals through the impressive Ian Poveda, CJ Hamilton and substitute Jerry Yates.
Forest substitute Ryan Yates headed a late consolation for Forest, who had made 11 changes for the tie, but it was a miserable afternoon for the visitors.
Appleton said: “We’ve done alright over the last five games since the World Cup break. We’ve put teams under the cosh at times and not been clinical enough.
“Even the defeat we had (last month) to Sheffield United, the last 25 minutes they knew they’d been in a game because we had them pinned back.”
Forest squandered a host of chances, with Sam Surridge the main culprit, while Blackpool goalkeeper Chris Maxwell made some decisive saves.
His effort to keep out Forest striker Emmanuel Dennis in a second-half one-on-one was the turning point as Blackpool made it 2-0 through Poveda soon after.
Appleton said: “The second goal was always going to be big in a game like this because of the quality they’ve got and for us to get that second goal was a bit of a relief.
“Obviously, you could see the confidence flowing through the players. Once the second went in, you could see the relief on the players and it freed them up a bit.
“I said before the game certain things are going to happen today. They’re going to have to have a bit of an off day and we’re going to have to have a good day.
“Max is going to have to make a couple of saves and we’re going to have to be clinical and fortunately we ticked a lot of boxes from that point of view.”
Former Oxford and Lincoln manager Appleton has enjoyed FA Cup success before in his career and knows how an extended run can transform teams.
He added: “To be fair, everywhere I’ve been, certainly in recent years, at Lincoln and Oxford. I had two or three really good cup runs.
“Fourth round with a League Two team, fifth round with a League One team and I think it does wonders for the club going on a run.
“That’s something we’re looking to do if we can. One it creates a little bit of momentum, but from a confidence point of view a result and a performance like today should do the players the world of good.”
Forest boss Steve Cooper admitted he had been ready to be quizzed for fielding an entirely different team following their midweek win at Southampton, which had lifted them out of the top flight’s bottom three.
Cooper cited a string of injures to key players for his wholesale changes, but refused to hide behind that after a chastening defeat.
“It’s unacceptable,” Cooper said. “It’s not good enough. It’s all of those negative words that you can think around it. I’ve said exactly the same thing to the players.
“We have to accept we fell short today, in every way, shape and form. Recently, we’ve had some good examples of what it takes to play well and win. We’ve showed a good example of the complete opposite today.
“I won’t even say we’ve got to learn from it, because that’s like saying today was OK, and it’s not. We’ve just got to make sure that never, ever happens again.”
Forest were punished for individual errors for Blackpool’s first two goals and Cooper did not pull his punches.
“I’ve said to the players, the individual mistakes for the goals we conceded are unacceptable – equally, the missed chances,” he said.
“Apart from Emmanuel Dennis, we’ve not even hit the target. They were absolutely clear-cut chances and for me, we accepted defeat far too early in the game.”