The Spanish tactician left the Championship club under acrimonious circumstances following his comments about loyalty last year and he says that the Swans supporters basically had the right to be upset with him as he guided the Latics to a 2-0 victory.
"It is understandable," Martinez said.
"I heard people say I lied to the fans - I never lied. What I said at the time was because I felt that way.
"After that I was interested in what was best at that moment.
"Right now I think fans will understand why I had to leave at that time and looking at the foundations they have, it has brought them stability.
"I am glad to see a strong side like Swansea City is ready to compete."