Vale entered the match with only one win in eight but an early strike from Jennison Myrie-Williams and a Lee Hughes goal was enough to seal a valuable three points.
The victory saw Vale cut Gillingham's lead to four points at the top and Adams is now hoping the win can spur his side on for the remainder of the campaign.
"I feel a lot of relief I think and I'm pleased for the people that matter - the supporters," he said. "We worked hard on a difficult surface but we did all the right things at the right times.
"It could have even been more comfortable but I think there was a real resolve about the squad. We would rather not have the situation that we have found ourselves in but they happen and what it has done is it has brought us closer together and it's a big result for everybody.
"I'm hoping that will kickstart us again. We realise the importance of these next seven games. The quicker we get to 70 points, the better and it will be a big psychological boost for us."