Substitute Zeki Amdouni volleyed home a last-minute winner to settle a largely forgettable tie and clinch Burnley a third-round clash at Salford.
But Vitinho, Aaron Ramsey and Ekdal were all forced off through injury, with the latter carried off on a stretcher following a second-half goalmouth scramble.
When asked about his players’ injuries, Kompany said: “One I think will be bad. It looked like it. I’ll take anything positive on that of course.
“In terms of Viti (Vitinho), we hope he’s not too bad. Certainly, it cost us a little bit this game.
“From what I’ve seen and watching the images, it looks knee for both (Vinho and Ekdal). There’s different degrees, it could just be a strain, but for Ekdal – we hope it’s not too bad. He was in a lot of pain.
“I really hope he’s not too bad, but there was a cost to this game for sure.”
Switzerland forward Amdouni, signed from Basel in July, was a 78th-minute replacement for Jay Rodriguez and fired home his first goal in English football in his third appearance for the Clarets.
“He’s got a real goal threat,” Kompany added. “I hope that’s one of many for him. That’s one exciting thing about our squad. I’m not saying in year one you’re going to be bursting the net every week.
“But in the future, potentially in our squad there’s a real goal threat. How long it will take I don’t know. Some guys are always dangerous on the pitch.”
Neither side created a scoring chance worthy of note before Amdouni’s late intervention and Forest boss Steve Cooper said his side “got what they deserved”.
He said: “We feel really short with our performance levels, both collectively and individually and certainly with the ball.
“I didn’t think we were going to concede a goal. The game had 0-0 written all over it. It wasn’t a great game obviously. Technically we were miles off it today.”
Johnson has been heavily linked with a move to Tottenham but Cooper insisted that was not why the Wales forward started on the bench.
“I know there’s a lot of speculation about him, but it’s not really affecting us at the moment and until we get told different we’ll deal with it and it’s business as usual,” he added.