The 35-year-old ends his 13-year spell at The Hawthorns this summer having helped the Baggies return to the top flight.
While the midfielder and club captain will spend next season elsewhere, Brunt insists the hard work starts now for Slaven Bilic's men.
Brunt says Albion must get their recruitment right this summer and continue to build if they are going to make an impact and retain their place in the top flight next season, which could begin in as few as just six weeks.
Brunt said: "Hopefully the club will go from strength to strength, recruit well for next season and build to stay in the Premier League.
"The hard work starts here, if you want to be a Premier League club you have to build and build on it as we have in the past.
"We have had a transition in the last couple of years and hopefully now the club can do it for years to come."
Brunt, the club's record Premier League appearance maker, came on as a sub in his farewell Albion appearance in the 2-2 draw against Queens Park Rangers, his 418th in all competitions.
But Brunt, who turns 36 at the end of the year, insists he still has another couple of years in his legs.
He added: "Obviously with the coronavirus stuff going on a lot of teams aren't too sure what's going to happen next year.
"I don't even think we're too sure when it's going to start.
"I feel OK, good physically, it's difficult recovering week in week out at my age but I haven't had to do that an awful lot this season.
"I want to play on, I've enjoyed the bits and pieces I've got through this year and I still feel I've got a year or two left in me and hopefully something will crop up."