The Teessiders have lost 10 of their last 13 Championship games and are now five points adrift of the play-off places having at one point been genuine contenders for an automatic spot.
Mowbray told the Evening Gazette: "I don't think anybody takes it harder than a manager at a football club, I would have to say.
"I have supported this club since I was a boy of six or seven. I know supporters take it very hard, I think we all do, and yet as a manager, you do feel as if the buck stops here, it is your responsibility.
"When you lose a match, you take it hard. You have to be resilient, you have to have a thick skin, you have to go again because generally there's another game pretty soon.
"But how am I? It's tough at the moment. It would be wrong to say anything else. It's not nice losing football matches, and we have lost too many football matches."
Middlesbrough defender George Friend, meanwhile, is refusing to give up on his promotion dream.
He told the club's official website: "With eight games left, we have got to believe that if it is mathematically possible, we can still do it.
"We are massively disappointed and we have just got to be better. Inside there [the dressing room], we were saying there are eight games left and we can still do it.
"But we know we have to improve on performances like that if we want to be where we want to be, which is getting promoted."