Laws' first League match since returning to the club, which fell on the sixth anniversary of his departure to take charge of Sheffield Wednesday, renewed hopes of supporters after the disappointment of Saturday's 4-0 humbling at Gillingham in the FA Cup.
The Iron had been on such a poor run of form, that Laws suggested the players were reluctant to celebrate in the away dressing room afterwards.
"I told the players to smile and enjoy it, without getting carried away," he said.
"The most important thing for us was to start winning games, and this has been a long time coming.
"But we are not getting carried away. We have won here but there are a lot of games still to play and this is one small step."
"Coventry on Saturday is another tough game, but if we're organsied as we have been here then we've got a chance."
Laws ruled out appealing the red card shown to Prutton, who will now miss the next three games.
"It's going to be a big blow, because centrally we're a little bit weak," he added.
"He's trying to retain the ball but has gone in a bit late, is it a red card? Probably not but you can't lunge into anything even more, even if there is no intent."
The club are still unsure as to the extent of David Mirfin's leg injury, with results not yet back from a scan.
Walsall boss Dean Smith, felt his side were low on confidence - a tale familiar to fans of the visitors.
"Scunthorpe have some good and experienced players, and if they had been playing like that two weeks ago then Alan Knill would still be in a job.
"We are on winless run at the moment and lacking a little bit of confidence, and in a young group that happens. There are two ways to go now - either sink or swim, and we have to get ourselves together and put it right."