The black, green and gold suffered an agonising 35-30 defeat at Kingsholm back on March 5, denting their Gallagher Premiership play-off hopes.
But they have since won five successive games in all competitions, propelling themselves back into the top-four picture.
And this weekend they will be hoping to further their European aims as they go up against Gloucester in the last 16 of the Challenge Cup.
"We went to Gloucester last month and played pretty well but didn't manage the last 20 minutes very well," Vesty said.
"We've got a score to settle there.
"When you're in knockout rugby, it's a fresh challenge, a new mindset away from the Premiership and it gives everyone a bit of a buzz.
"Something is on the line this weekend because, to state the obvious, if you win you're through and if you lose you're out."
Last month's defeat at Gloucester was actually the last time Saints lost.
So how much progress does Vesty feel his players have made since then?
"I actually think during that period we were playing pretty well," he said.
"We lost some big moments and we didn't manage some things we could have done but we weren't a million miles away.
"Yes, you lose three games on the bounce and it hurts you and it hurts you in the league, but you know the performances aren't far away and as a group we felt that.
"When you're striving to do the right things and everyone knows they're the right things, you know it's not far away.
"In the past few games we've done a couple of little bits a little bit better and we've been on the right end of the results."
There will be something of a changing of the guard at Saints this summer with boss Chris Boyd leaving and the likes of Teimana Harrison and Api Ratuniyarawa also departing.
And Vesty said: "People have given the best years of their life in playing for Northampton.
"And with Boydy leaving at the end of the season, it would be a great way to send them all off and give them something to be really proud of.
"We all want to win silverware - and this would be a great year to do it."