Hodgson will leave at the end of the season to take up the England post.
Brunt told Sky Sports: "It would have been easy for us to roll over (at 2-0 down) because we don't have an awful lot to play for, but that's not the group we are and that's not the way the gaffer has got us set up.
"Obviously he wants to go out on a high and we want to finish the season on a high, on as many points as we can."
He added of Hodgson: "He's a fantastic coach, he's so experienced. He's a good man as well. He will be missed and the club have got some large shoes to fill there.
"If you look at England they've got some of the best players in the world so if they can buy into what he's all about I'm sure they'll do very well this summer."