Winger Etienne Esajas fired the Iron into an early lead with a sweet left foot shot from the edge of the box for his second goal in successive home games.
But they then wasted a catalogue of chances before substitute Sam Winnall finally eased any nerves in the 90th minute.
"A one-goal lead is never enough and we were made to sweat a bit in the second half," confessed Laws. "When you miss chances like we did, it gives the opposition something to hold on to.
"Credit to Cheltenham, in the second half they were causing us problems and my heart was in my mouth when they were awarded a free-kick right on the edge of the box.
"I must admit I thought it might have been inside the box but the video has shown the referee got the decision exactly right.
"To be honest, we should have had this game dead and buried in the first half, which we dominated for long periods.
"We needed that second goal to kill the game off and I am pleased for Sam Winnall that he came off the bench to get it for us.
"He has responded well to being left out of the team and that is exactly what I want to see from him.
"I left him out because I thought his performances had dipped in the last few games and I thought it was time to take him out and get him ready to go again.
"Sam has been snatching at his chances and could have had a hat-trick in this game."
Laws was also pleased with a debut performance from midfield man David Syers, signed on loan from Doncaster.
"David has not had any first-team football this season so his fitness levels are not what they might be," said the Scunthorpe manager. "But I was pleased with his performance, he got forward well and could have had a couple of goals himself.
"He showed great energy before tiring in the second half - and I am sure he will only get better for us."