Bellamy scored two goals in the aggregate 4-3 win at Eastlands on Thursday, dedicating both to his late cousin.
The brace - netted inside seven minutes in the second half - helped ease City through to the last 16 of the Uefa Cup where they will face another Danish side Aalborg.
Heaping praise on his striker's character, Hughes admitted Bellamy's decision to play was a huge benefit to City's progress.
Character"Craig showed great character as he has done for many years," said Hughes.
"He showed real mental strength to play after a close family member had passed away.
"It was touch and go whether he was in the right frame of mind to play. He wanted to play and we benefited from that.
"Under difficult circumstances he has come through and made the impact we hoped he would."
He added: "My satisfaction comes with winning the game and progressing into the next round.
"We are delighted with that as some big names have gone out. I think we deserve a bit of credit."
ToughBellamy later revealed he had been hit hard by the death of his cousin.
"I lost my cousin, one of my closest friends, on Thursday morning," said Bellamy.
"It was a hard day for me, for my family and his family. I'll miss him dearly and I'd like to dedicate this game to him and the goals as well."