The Pole, on a season-long loan from Liverpool, suffered a sickening collision with Terriers captain Chris Schindler in the 71st minute, prompting a 12-minute delay while medics attending to him amid worrying scenes.
The game eventually got back under way and there was further drama when substitute Steve Mounie headed home a 96th-minute stoppage-time winner to secure a first win in 2020 for the relegation-threatened Terriers.
Cowley, whose side had led thanks to Karlan Grant's 13th goal of the season on 24 minutes - with an own goal from Richard Stearman levelling proceedings on 66 minutes - said: "We are obviously concerned about him. It was a nasty one, a very nasty one.
"He was knocked unconscious for a period of time; I am not sure how long. He did not know where he was when he came around.
"Our thoughts are with him this evening. He has gone to hospital. He has got good care around him now and we are just hoping that he recovers. It is the life of a goalkeeper, I suppose.
"You never want to see that on a football pitch, certainly with one of your young players."
Cowley admitted that his side's reaction to Hull levelling and to the serious injury suffered by Grabara was testament to their character on the night.
He added: "That was the most pleasing part of this evening.
"Maybe in two, four or eight weeks ago, we would have maybe gone under in that moment.
"We talk about the minerals and substance that you need to be a good team and we showed it in that moment.
"Credit to the players. As you can imagine, it was an emotional moment when they see one of their team-mates down injured with the way he was and for them to take on the information and implement it in the way they did was credit to them.
"The break in play probably helped us as it allowed us to get organised and change the shape and the way we were pressing."