The Belgium striker scored the only goal of the game as Everton ended a run of eight games without a win by defeating Crystal Palace on Saturday, consigning Alan Pardew to a first defeat since taking over at Selhurst Park in the process.
And Martinez singled out Lukaku – who grabbed his first goal in eight league games – for particular praise.
"I was really pleased with Romelu's performance. He loves taking responsibility and as we know, as a striker, he has the potential to be one of the world's best." said the Spaniard.
"I think his form was infectious in that forward line, he was powerful and looked really fresh and that was pleasing.
"When you've got a striker like Romelu in that type of form – it really sets the standard for the play.
"He's an incredible footballer at our football club and he's a responsible young man – I think sometimes we forget that he is only 21.
"He came back from the World Cup and it is always difficult to pick up your fitness but now he is fully fit and ready to take on that responsibility."
Everton, who returned from a mid-season trip to Qatar in midweek, got off to a flying start when Lukaku bundled home his eight league goal of the campaign from Steven Naismith's deflected cross after just two minutes.
Palace threatened throughout, but the visitors stood firm to end a five-match losing streak on the road in the Premier League.
"We had to be perfect to get the three points today because we were against a team that are full of confidence," Martinez added.
"We managed the game really well. We carried a good threat, maybe we should’ve scored a second goal but we did brilliantly.
"We've got a really responsible group of players. We wanted to enjoy our football and show what we can do and it felt for a while we couldn’t do that– so it was very pleasing."
