The Chelsea loanee scored twice on his home debut as well as providing an assist for Ross Barkley, and Martinez heaped praise on his new acquisition after an excellent display.
"It's a loan deal for the season. That's the case for Gareth Barry and for Romelu. I could be sweating now if it wasn't," he told reporters.
|6/1||Everton are 6/1 with BetVictor to finish in the top four this season
"When he holds up play with his back to goal he is a focal point. His relationship with Ross Barkley was magic at times.
"He's a great goalscorer. I want him to enjoy his football, develop and become as good as he can be."
The result sees Everton climb to fourth in the Premier League table after an unbeaten start to the campaign, and despite a Newcastle fightback in the second period, the former Wigan boss was thrilled with his side's performance.
"We were very, very good in the first half," he added. "We defended very well and kept Newcastle to very little threat.
"From that point on some of the attacking play as fascinating. The link-up play between Romelu, Ross and Kevin Mirallas was at its best.
"After we conceded the first goal I was very pleased with the way we controlled the game. We showed style in the first half and grit in the second half for a well-deserved three points."
Newcastle boss Alan Pardew, on the other hand, was highly critical of his side, though he was given some heart by their resurgence after the half-time break.
"It would have been fortuitous for us if we'd got something from that game because in the first half I'm afraid that wasn't good enough from us," he told a press conference.
"The second half was much more like it. We showed a lot of pride and a lot of passion.
"We won some headers, made some tackles and made some forward passes, which helped. We managed to get two goals and almost get something out of it."