An early goal by Lee Hughes and one in each half for winger Ashley Vincent was easily enough for Vale to see off bottom club AFC Wimbledon 3-0 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.
"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."
- Sports & Recreation
- Ashley Vincent
- Lee Hughes
- AFC Wimbledon