Christian Nade and David Templeton could have made the game more comfortable for Hearts only to squander decent chances, but previously in-form St Mirren posed little danger from start to finish and rarely threatened an equaliser.
The win was a welcome one for Hearts after the disappointment of their Cup exit at Aberdeen last week and consolidated their fifth place in the table, keeping alive their hopes of breaking into the top four.
Laszlo said: "The spirit was good and we had some good chances and I was a little disappointed we didn't take them.
"We had a period in the second half of about 20 minutes when we should have scored the second and therefore it would have made the game easier as we would have had more confidence.
"But we must remember we had a lot players coming back from injury such as David Obua, Ruben Palazuelos and Jason Thomson so we must be pleased.
"We had the discipline within the team and as a result we didn't concede so we won the game. It was a '1-0 game' so we had to have the discipline to stay behind the ball and not give our opponents any chances. That's what we did well.
"They had a couple of corners which were maybe a little bit dangerous but nothing apart from that and to come back from what happened in Aberdeen was very good.
"We were down after that game and we lost because we didn't have the tactical discipline we had seen in the previous five games. But we had our discipline today and it showed that the team can do this if it has the right concentration.
"In Aberdeen we didn't and we lost the game because we had the ball and gave our opponents the chance to break from their own half and score."
St Mirren manager Gus MacPherson had no complaints with the penalty decision from referee O'Reilly.
MacPherson accepted it was the correct outcome and admitted his side found it impossible to break down the resolute Hearts defence once they had the lead.
He said: "We've won a couple of games 1-0 and today we lost 1-0. It was a very scrappy affair because that's what you're getting at the moment due to the pitches not being in great nick.
"We made a mistake in a defensive area. I didn't see a nudge or anything so it was definitely a handball and I've got no complaints.
"Hearts are a good defensive unit and are very difficult to break down. If they get that goal in front they shut up shop. We'd bits of pressure but nothing sustained.
"Hearts defend well when they get in front and it is frustrating but they defend the width of the goal very well.
"That's just how tight the games are at the moment. So many are being settled by one goal or a set piece because the teams are all so closely matched."
Source: Team Talk
Source: Team Talk