Roberto Martínez has said Everton plan to build around Romelu Lukaku, Ross Barkley, John Stones and James McCarthy this summer and need to strengthen only in two or three positions to “create a winning team”.

The quartet impressed in the 3-0 win over Manchester United on Sunday as Everton’s belated recovery from a turbulent season continued into a sixth game unbeaten. Martínez’s side have taken 16 points from the past 18 having hovered six points above the relegation zone after a 2-0 defeat at Stoke City on 4 March.

With no European football on offer at Goodison Park next season, and the young assets emerging from a difficult period, the Everton manager expects interest in players such as Lukaku and Barkley from rival clubs. However, he does not anticipate any major sales and insists his main transfer activity will centre on a few specific incomings.

Martínez said: “I don’t want to lose anyone this summer. We worked hard last summer to have continuity and to get Romelu Lukaku and Gareth Barry on a permanent basis, as well as new contracts on Ross Barkley and John Stones. We made huge investments in those two young player so our focus is not to lose anyone this summer and to add two or three to the group.

“But, in the same way, if someone doesn’t want to play for Everton we need to be in a position where we can become stronger at the end of it. But that’s talking generally, nothing to do with our squad. I am not concerned that if we lost Ross Barkley we would lose all the work that we have put in [over the past two seasons] because we don’t want to lose anyone.

“Looking at the team and the way we are playing at the moment, I think we are learning our lesson and have a more mature group of players than last season but we want to create a winning team. I think we are getting very close. Those four [Barkley, Lukaku, McCarthy and Stones] are better players than they were 10 months ago because of the experiences we have been through.”

The quartet are under long-term contracts and Martínez’s priority is to strengthen in attack, where Steven Pienaar’s injury problems have created a void on the left, and the manager wants more creativity behind Lukaku. “We have got all these players on long-term contracts so it is not as though we are facing a situation where they are out of contract,” he added.

“We control the situation. In terms of the players we bring in, it is very much about the positions we need. I don’t think it’s about glamorous names, it is about players who can fit the specific positions for what we are trying to do. I’m very excited about what we have already got at the club.

“It’s quite clear we don’t need anything glamorous apart from getting two or three players who can fit into how we play while giving us something we have missed this season.”

The Everton manager claims to have shelved plans to sign a goalkeeper. “I am very pleased with Tim [Howard] and Joel [Robles] for next season and we’ve got high hopes for Russell Griffiths plus Jindrich Stanek will have a bigger role next season,” said Martínez, who has not given up hope of the England Under-21 international Luke Garbutt remaining at the club. The promising left-back is out of contract this summer and has seen his first-team chances restricted by Leighton Baines.

The manager said: “I want him to stay at Everton but in the same way you cannot force players to stay if they don’t want to stay. I hope that we can solve it in the summer and work together in that respect. You need to accept what the player feels as well.”

The Costa Rica international Bryan Oviedo, meanwhile, will miss the rest of the season plus the Concacaf Gold Cup in July after fracturing a metatarsal in training.