Sky Sports exclusively broke the news that Boro lodged a £4million bid for the Belgian international on Monday.
But Genk rebuffed their attempts and their sporting director Dirk Degraen described the offer as 'timid' - something which Mowbray is not entirely happy with.
"I don't know if it will be revived," he said of Vossen.
"There have been quotes from their club, disappointing quotes. We have been respectful of their club. He would have done well for us and played most weeks.
"The word timid, which they suggested, was a bit disrespectful.
"He has just signed a new contract so it's not a case of waiting and there are other targets, we missed out on others."
Mowbray also insisted that, just because Boro found £4million to bid for Vossen, they do not have a huge amount to splash around on the squad.
"Every deal has to be treated on its merits," he told the Northern Echo.
"We have to be creative, so it doesn't mean we have a lot of money to spend. We might feel there is an area of the pitch we could weaken to strengthen a part of the pitch we feel needed strengthening."
Mowbray was happy with the business he did do on deadline day, bringing in Kei Kamara and Jacob Butterfield.
"You have to build carefully and patiently," he said.
"The team is improving and if another player comes up and we feel he can improve the team then we will move on it.
"The danger is everybody wants everything built today. The proof of the pudding will be in the eating."