Lukaku opened the scoring on the stroke of half-time, sending a thumping header in from six yards, before doubling his tally after the interval tapping in a rebound after Kevin De Bruyne had an effort saved.
Those goals took Lukaku to 25 goals from his past 21 Belgium matches, though were it not for a couple of bad misses, he might have scored four on the day.
Martinez felt the supporters showed their appreciation for him regardless, but the head coach wants the much-maligned Manchester United forward to take advantage of his hard work even more often.
"I appreciated the love fans have shown towards this national team and Romelu in particular," he told reporters. "He is a boy who has been very successful these last three seasons. He creates opportunities and scores a lot.
"I see him very disciplined, and during this international break he has displayed a lot of desire. Sometimes, I'm sad when I see that Romelu does not take advantage of his play on the pitch."
De Bruyne was the standout performer in the match, though Martinez was keen to share the praise around.
"It's not a single player match, everyone contributed to this victory," he said. "Kevin did indeed have a big influence, he was both active and patient.
"But Eden Hazard was also very important, taking responsibility, while Lukaku made the net shake twice.
"When I see how Thorgan Hazard is progressing - he was not even in the 23 at the beginning of my term - how Thomas Meunier held 90 minutes after Timothy Castagne's match, I think we have plenty of options, and that's fine.
"Do not forget the hard work of the three central defenders, who prevented Scotland from scoring against us."
The match brought a first defeat as Scotland boss for Steve Clarke, but overall, he was left satisfied with what he saw from his side in his debut international get together.
"My impression is that I saw over the 10 days that I've got a really good group of players who are really committed to their country," Clarke said. "They want to get better and they want to improve.
"We were competitive in that game against the best team in the world, ranked number one, so there's a lot of positives, but obviously we're professionals and we don't like to lose the game."