Vokes netted twice in 10 first-half minutes after Scott Arfield had opened the scoring for the Clarets as Burnley put an abrupt end to Forest's 14-game unbeaten run in the Championship.
Djamel Abdoun grabbed a consolation goal for the visitors late on, tapping in a rebound after Tom Heaton saved his penalty, but Burnley cruised to victory.
Dyche is not getting carried away by his side's promotion chances, with the result keeping them in second place, but he is impressed with Vokes' form.
"He is enjoying his football. He is more than just a big man. He's got awareness, good feet and we are certainly enjoying working with him," the manager said.
"I don't think a game is over at half-time, but I think the performance warranted it to be. I thought that was top class, I thought we were absolutely first class.
"That first half was exceptional at times, it could have been more, maybe should have been.
"There is massive expectation at Forest and you can understand why. They have a manager who understands the level. Whatever team they put out you know you are in for a game. I thought we dealt with that very well today.
"It (the promotion talk) is only outside noise, we focus on what we are doing. The mantra has been clear since pre-season, one game at a time. Never gone beyond that, they are hungry every time the whistle blows."
Forest boss Billy Davies felt Burnley struck at just the right time to end their impressive league run, but admitted his side were second best.
"They got us at the best time possible," he said. "We are missing so many players. We lost Andy Reid yesterday with a calf problem.
"Burnley got us at the right time. That is not taking any credit away from them because in the first 45 minutes their team competed, worked and battled much better than we did.
"We had a certain game plan before the game. To come to Burnley you have to play a certain way. You have to prepare to face a certain type of game and unfortunately for the first 45 minutes they didn't listen.
"They played a very direct game that puts you under pressure and quite simply we never handled it.
"We didn't do what is necessary against this type of team. We had better success second half because we changed our game. We were more aggressive, we were more energetic. But it was too little, too late."