Hovering just above the relegation zone, a point against an in-form City side would have moved Forest six points clear of West Ham in 18th.
But Cherki crushed their hopes as he slammed home a half-volley, drilling the ball from the edge of the box through the legs of Gibbs-White.
Forest players were quick to complain to referee Jones, arguing that Gibbs-White had been knocked over by Nico O’Reilly and prevented from blocking Cherki’s strike.
“Morgan Gibbs-White quite clearly gets pushed to the floor and the same player is involved in blocking the ball,” Dyche said.
“But he can’t block it because as he jumps up, it goes through the bit of his body which he would have blocked it with. Whichever way you look at it it’s a foul.”
The VAR checked the goal, but ultimately allowed Jones’ on-field decision to stand.
Dyche added: “They’ll say, ‘Yeah, the ball wasn’t there’. And you go, ‘OK, so if the ball’s not near the keeper and you push the keeper to the floor, is that going to be a foul then?’
“We all know it is. I can’t work it out. And then they score from it, which is the double whammy.
“I’m a big fan of VAR – I can’t work out how you can’t get that right.”
Former official Darren Cann told BBC Match of the Day: “The video assistant referee naturally checked the goal and concluded that no ‘clear and obvious’ error was made. I agree.
“This was a decision that will split views – some will agree it’s a good goal and others will think it was a foul. Therefore the ‘referee’s call’ of goal should stand.”