The Baggies face Bolton on Sunday before entertaining Arsenal a week later, and Brunt is keen to give Hodgson a winning send-off.
"I don't think there's any real surprise among the players that he's got the job," said the midfielder.
"We're all delighted for him, he's been brilliant since he came in. His experience and his knowledge of the game - it really sorted us out at a time when things were going downhill a bit last season.
"What we want to do now is finish the season on a high note. We want to beat the points tally from last season and the gaffer will want us to finish in the top 10.
"A lot of fans will be coming up to Bolton because the last away game of the season is always a bit special. With them still being in the relegation battle we owe it to the clubs down there to put a shift in."