The full-back delivered an assured performance at left-back and kept one of Japan's principal threats, midfielder Naohiro Ishikawa, quiet during the 2-0 friendly defeat.
Having been a late addition to the Scotland squad following the withdrawal of Celtic's Danny Fox, Wallace's composure on his debut was one of the features of the match and proved his capability to excel on the international stage.
"I was happy to see Lee in his first national team game. It was important for him to make the trip with Scotland to show that this is definitely a player for the future," said Laszlo.
"I know the score was 2-0 to Japan and maybe it was not the best game for the national team, but personally I was satisfied with Lee and his performance. I think this is the most important step. Other people can analyse the performance and the result but I am happy to see a person from Hearts in the Scottish squad." Larry Kingston played 85 minutes of Ghana's 1-0 World Cup qualifying defeat to Benin yesterday and is due to report back to Riccarton this week.
Meanwhile, Hearts teenager Craig Thomson has won the Clydesdale Bank Young Player of the Month award for September in recognition of his faultless displays at right-back. The 18-year-old attributed his early success to idolising David Beckham but also revealed some useful advice from Tynecastle predecessor Robbie Neilson.
"I've always watched David Beckham and looked up to him as a role model," he said. "Obviously I just try to copy what he has been doing. I read his autobiography and he said he used to hang tyres from the goalposts and just whip the ball in. I've never had any tyres to do that but I'll do things like put bibs in the corners of the goals and try to hit them."
"Growing up I idolised Beckham but Robbie Neilson was a role model who would always help me out. If I was doing anything wrong he would tell me and he was different class, really. Recently, I've started to look up to Sergio Ramos and Dani Alves. Ramos started playing centre-half but going forward he is different class and that's what I want to do – keep pushing forward as much as I can."