Goals from Richard Hinds and Matty Sparrow in the closing stages of the first half were enough to seal United's first win of the season.
Laws said: "For the first 20 minutes they set about us, but we got a second wind.
"We had to defend really well and our keeper had to make some great saves to keep us in the game.
"We had to weather the storm but after that we got into our stride and eventually found it comfortable.
"Goals really knocked the stuffing out of them. We actually had the better chances towards the end of the game, but it was nice to take our first half ones.
"Once we got in front I asked for us to pass with purpose and the wide players to tuck in and we did that well. When you consider we had Ian Morris and Daniel McBreen making their debuts as well, it was a great result."
Gillingham fans called for chairman Paul Scally to resign after the loss, but manager Ronnie Jepson insisted he should be the target.
He said: "I take full responsibility for the result - the buck stops with me.
"It was very frustrating as we were excellent for the first 30 minutes and created so many chances but we had to stick them away.
"The confidence was really hit by the two goals. The lads showed plenty of commitment in the second half but we needed more nous on the ball. We kept at it but there was too much huff and puff.
"When we have teams on the rack like we did tonight we have to score. Had we done so then I think we could have gone on and won.
"But we'll stick with it, regroup, and hopefully the lads will start firing soon."