Their 3-1 victory against Carlisle, on the night of their 100th anniversary as a professional club, was the first time since March 2009 that Scunthorpe had won three games on the trot in front of their own fans.
"That is an awful long time to wait for us to do it again," said Laws. "We have to dedicate this week to the supporters for their suffering over the past four years."
Striker Akpo Sodje struck twice for Scunthorpe to take his tally to four goals in the last three homes games. And skipper Paul Reid was also on the mark as his improving side pulled five points clear of the npower League One relegation zone.
"The players have always been focused on what they had to do in these last three games - and they have delivered," said Laws.
"Psychologically they are all feeling much better about themselves now. Belief is the key and when you start winning games at home it does wonders for your confidence.
"That is the magic dust that we have been looking for, winning games again at home.
"The players were beginning to feel apprehensive about playing in front of their own fans, but they are beginning to enjoy it again now.
"Now we have got to press on. Survival is still our number one aim this season. We can't afford to rest on our laurels now."