Pablo Fornals and Saïd Benrahma both beat Dean Henderson with long-range shots, only to see the ball bounce back to safety off the underside of the crossbar, while Declan Rice had a penalty saved by the Forest keeper.
Fabiański told whufc.com: “We're very frustrated.
"We knew before the game that it would be tough and there would be a lot of energy in the crowd, because obviously it was the first home game for them in the Premier League for a while.
“So we were expecting a big battle and that's how it was from the first minute. I would say they were better than us in the first half, but once the second half started we had the much better chances.
“We hit the bar twice, we had a penalty saved by their keeper, so we're very disappointed that we didn't take anything from the game."
He added: “Like I said you're always disappointed when you concede a goal, so that wasn't a nice way to finish the first half.
“We have the experience to know that there are no easy games in the Premier League.
“You get punished for the little things and that's maybe what happened today, with us not taking our chances and conceding in a way a soft goal.
“You have to earn the right to play football in the Premier League, and Forest took their chance [and that's why] they came away with the win."