Howard has been strongly linked with a move back to Major League Soccer, with Colorado Rapids said to be keen to sign the 36-year-old.
"Tim, in the first season I arrived at the club, had a phenomenal campaign," Martinez said.
“And if you look at the clean sheets and defensive record we had, he had a massive say on that.
“Joel (Robles), from the beginning, competed in a very healthy manner but I must say that Tim Howard is one of the most complete, experienced players I have ever worked with.
“He knows how to affect people around him, he never blames anyone, he always wants to get better, he welcomes the competition and the reflection I have seen in Joel Robles, and the way he is growing, is down to the environment Tim Howard has created at Finch Farm and I will always be very, very grateful and every fan should know what Tim Howard has been doing behind the scenes and when he is on the pitch."