Browne set the Lilywhites on their way to the 4-1 win, volleying them into a 24th minute lead from a Brad Potts cross.
Emil Riis then bagged a hat-trick, although his first has been officially credited as a Dael Fry own goal.
It was a dominant performance from North End against a Boro side who went into the game still in with a chance of making the play-offs.
Browne said: “It was a good way to finish the season, a performance like that is something we had been looking for all season.
"We left it late with it being the last game but it was a nice way to finish off.
"We wanted to win more than anything today with Paul Huntington leaving. Thankfully we did that and Hunty went out in good fashion.
"Hunty has been a fantastic player for this club and it’s sad to see him to go, he’ll be a great signing for someone.
"With Middlesbrough in with a chance of the play-offs, it was all to play for. We had to be up to the task and it was good to take a two-goal cushion into half-time.
"We then responded really well when they scored early in the second half. Middlesbrough could have shifted the momentum in their favour after their goal but we dealt with that well.
"Going into next season, this is the sort of performance we are looking for a lot more often.”
It was a fourth goal of the season at club level for Browne, with one for the Republic of Ireland.
A better goal return is his target and he hopes scoring in successive home matches is a sign of things to come in 2022/23.
Browne said: “In the last couple of games I’ve found myself in the box a bit more. That is what I need to do to add more goals and assists.
"For my goal I saw the ball late, it sort of hit my chest and fortunately the volley was a good one it went in.”
Browne has backed Riis’ claim for a hat-trick and played a captain’s role in making sure it was the Danish striker who took the penalty for the fourth goal.
"I hope Emil is credited for the hat-trick because I took the ball off Cameron Archer for the penalty,” said Browne.
"Cam played really well and he deserved a goal but I took the ball off him because Emil was on a hat-trick in my eyes.
"Emil has has a fantastic season, a lot of his goals have been self-made, he works his socks off and is a nightmare for defenders.
"To have a 20-goal striker is brilliant, bearing in mind where we are in the league table and how we haven’t played well in some games.
"Emil’s goals are a reward for his hard work and he’s developing really well. I’m sure there will more goals to come from him next season.
"For me, it was definitely an Emil hat-trick and I’m sure their player doesn’t want the own goal.”