On what was his first start since September, Jelavic scored for the first time since March, netting in each half at Goodison Park as the Barclays Premier League hosts cruised into the fourth round.
Other clubs have made inquiries about the Croatia international, with Sky Bet Championship promotion-chasers QPR reportedly being one of them - although Martinez said he had not held talks on the matter with Rs boss Harry Redknapp.
There has also been interest in Everton's Holland defender Johnny Heitinga, who turned down a switch to West Ham earlier this week and made only his third appearance of the campaign when he came on as a late substitute in the QPR contest.
With both players hoping to feature at the World Cup this summer, Martinez has made it clear he feels it is only fair that he considers offers for them.
But regarding Jelavic, the Spaniard said: "I don't want to sell him - I don't want to lose him now, but I understand it is a key moment for him.
"Put it this way - if the World Cup was not in the summer, this situation would never be in place.
"It (any move) will not be a loan situation. That wouldn't allow us to replace Jela at all, so I don't think that would be right for us. It has to work for the player, but more importantly, for us as a squad.
"The only possibility would be a permanent move that would allow us to bring another striker in, so we are able to be as strong as we are with Jela."
Martinez also said that, ideally, Heitinga would not be leaving, and added of the pair: "If people think they can just get them on the cheap, or as a good deal, they will never move - it is a very clear situation.
"I think they have a very clear value in the market and if that gets matched, then there will be a conversation to take place."
After his second goal, Jelavic blew the chance to complete his hat-trick when he missed a penalty by chipping it against the crossbar.
On the frontman's overall performance, Martinez said: "It was very, very good.
"He is a bit frustrated that he couldn't get the hat-trick - I did feel his performance deserved it.
"I thought he looked very sharp and that his movement was terrific in the box.
"He showed that he has been working really well in training and that he has been frustrated with a lack of minutes due to the great form of Romelu Lukaku.
"To see him on the pitch and enjoying his football, scoring two goals and performing like that, is very pleasing."
Asked if he had been surprised by the penalty chip, Martinez said: "I was, because he has not done that in training.
"He has never chipped the goalkeeper before, but that is down to the confidence in those situations.
"Unfortunately, when you make the decision, you need to make sure that the ball hits the back of the net, and it is a bad decision because he ends up hitting the crossbar.
"But I don't see any more of a problem than that."
Ross Barkley put Everton 1-0 up in the 35th minute and, after Jelavic's brace (44 and 68) and failed effort from the spot, Seamus Coleman wrapped up the scoring with 14 minutes to go.
QPR seemed entirely overwhelmed by their opponents, and Rs assistant boss Kevin Bond said: "Not making any excuses for us, but I think we were playing against one of the top sides, and they played very well, making it very difficult for us.
"We couldn't afford to come here and be too gung-ho and we felt we needed to try to stay in the game.
"But the pressure was growing, with them getting opportunities.
"We held out as long as we did, but the longer the game went, you did feel that it was only going to be a matter of time (before Everton scored).
"I think in order for us to maybe do something about it, we needed to come in at half time only 1-0 down, and I think the second goal almost settled the game as a contest really.
"It is disappointing, but this is not going to define our season.
"Not trying to wash over the defeat but, hopefully in the grand scheme of things, this won't have too big an effect on what is our main aim."
Asked about Jelavic, Bond said: "If you read the papers, he would appear to be on our radar.
"I can't say (whether or not QPR are interested in Jelavic), but it would be fair to say that the manager is looking for some striking options."
- Sports & Recreation
- Johnny Heitinga
- Barclays Premier League