"It was a tough game for us but we expected that coming to Spotland because they have had a good start to the season, but our confidence is high at the moment," Laws said to waiting media after the match.
"Coming in at hlaf-time I thought we were possibly the better of the two, it was a slow game and we stepped up the tempo in the second half."
After Matty Sparrow was shown a straight red card, for which he must now serve a three match ban, United were under the cosh for the final half hour but Laws was a relieved man that the defence held firm - despite conceding a late consolation goal.
"It's not often that that happens to us but we're playing well and we deserved it," he added.
Meanwhile Rochdale manager Paul Simpson was not a happy bunny, laying into his players after the defeat: "This is the worst week since I joined Rochdale. We practised things in training and then forget about them when we're in a match."
"We have some sorting out to do."