An early goal by Lee Hughes and one in each half for winger Ashley Vincent was easily enough for Vale to see off the bottom-placed Dons and record a sixth win in eight games. But Adams said: "We've achieved nothing yet. We've got another difficult game at Barnet on Saturday and we will now start to prepare for that.
"We are not cocky and strutting around like peacocks. There is a steely determination and pride about us to do things right and see the job through. There is real confidence that we can give anybody a game and it's up to everyone else to try to catch us if they can."
He continued: "We've produced another thoroughly professional performance. There were some terrific individuals out there, but the most important aspect is the team and collectively we were very good.
"I was bit surprised that Wimbledon set up with a defensive shape, but we soon got to grips with it and enjoyed a very good night. If I was at the bottom of the table I would want to go out and win a game, but what other teams do is, of course, up to them."
Wimbledon boss Neal Ardley said he accepted a large chunk of the blame for his team's first defeat in six games.
He said: "I'll take the rap because I took a calculated risk by playing five at the back and it didn't work. Vale's front four are the most potent in the league, their record tells you that, and I thought the best way to combat them was to change our tactics.
"It's a big pitch and I went for pace up front with Rashid Yussuff, but we soon gave a poor goal away from a set piece and it was a very difficult night after that.
"Vale are a very good side and they played a lot better than us. There weren't really any positives to take from the game, but we've got to draw a line under it and move on.
"There wasn't a lot of belief, but I've got a lot of good characters in the dressing room and I'm confident we can bounce back and be all right."