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."