The Spaniard has been linked with a number of his former players after sealing a move to the JJB Stadium.
However, Martinez intends to remain "honourable" in the transfer window.
He said: "I will never move for Swansea players unless they are in the market or other clubs show an interest.
"I would never go back to Swansea just to do that and pinch players. Now I am at Wigan we will not do things that are not honourable."
Some Swansea supporters have voiced their discontent at his departure, but Martinez takes great satisfaction from his time in Wales.
He said: "If the fans are disappointed, it is because they enjoyed the last two and a half years. I think it is the moment to look back and see how successful Swansea have been.
"I gave everything to try to bring success on the pitch, to play in a certain way and improve the club. I think we achieved that.
"In that respect we should all be proud together. Who comes in to manage that club is a very lucky man. From a distance I will be cheering, hoping Swansea take the next step."
Martinez does not have the UEFA Pro Licence, a requirement of managing in the Premier League, but is working towards it.
Chairman Dave Whelan is adamant the authorities will grant dispensation to his new man.
Martinez added: "You need to get the qualifications. It is vital. I am looking forward to finishing the A licence.
"There is a need in the modern game to do that. I hope I will complete it very soon."
Assistant manager Graeme Jones, who scored a club record 33 goals in the 1996-97 season in the old third division, is thrilled with the progress Wigan have made.
He said: "We could see the potential at the time and Dave Whelan's backing has made all of those dreams come true.
"To see us now in the Premier League and doing so well is absolutely fantastic. Now it up to us as a management team to keep the story going."