Goals from Arthur Gnahoua, Adam Phillips and Cole Stockton gave Adams a first win since returning as manager to the club.
As well as being happy with the points, the manager was delighted with the performance of his players, who dominated from start to finish.
He said: “It was a really good performance from us.
“It’s the best performance we’ve probably had since I came back to the football club.
“The players played really well and we controlled large aspects of the game.”
Victory, Morecambe’s first since January, saw them climb to fourth-bottom in League One.
They remain two points from safety with half-a-dozen games remaining, the first of which sees Oxford United visit the Mazuma Stadium on Tuesday evening.
With bottom two Doncaster Rovers and Crewe Alexandra both beaten at the weekend, it looks as if Morecambe, AFC Wimbledon, Gillingham and Fleetwood Town are in a four-way scrap for the final two relegation spots.
Of those four sides, only Gillingham have a worse goal difference than the Shrimps.
Adams added: “I think we could have scored a lot more goals, which was the only disappointment really.
“More goals will have helped our goal difference, which could be important at the end of the season.
“That’s why we were trying to push to get some more goals at the end.
“We’ve got three though and we kept a clean sheet to beat a very good Burton Albion side and we move on to Tuesday.”