Fellaini, who has been heavily linked with a move to Manchester United alongside team-mate Leighton Baines, scored an extra-time winner as the Toffees won 2-1 at Goodison Park.
After the game, Martinez refused to be drawn on the future of either pair - but made clear his feelings on the transfer window encroaching on the football season.
"The two players have been true professionals and that is what I want," said the Spaniard. "They are dedicated to the club."
"It is a circus when the transfer window is open and the games are going on. If the competitive games weren't going on I could sit with you here and talk about transfer targets.
"At the moment I really feel for the game. We are concentrating on rumours too much. There is nothing to tell. If there is anything to tell we will tell our fans.
"We are working to try to add a few new faces in the window but I hope the authorities will look into it and don't allow this to happen again. Next season will be even worse with the period of transfers and the games overlapping."
While Fellaini grabbed the glory in the end, it had looked as though it would be Stevenage's night when Luke Freeman gave the visitors a first-half lead.
But Gerard Deulofeu came up with an equaliser on his debut early in the second half and the Belgian popped up with the winner in extra-time - one Martinez felt was deserved.
"We deserved to go through," he said. "Marouane Fellaini gave us the push we needed but the headlines should be about how well Stevenage played.
"It was a typical cup tie. Stevenage were really really good, a well organised team. The first goal is always important. The goal was a little bit of a mistake, a misunderstanding.
"From that point on, I thought we were very good in two thirds, but in the final third we were at times naive. At times we didn't show enough sharpness. I couldn't be happier in the manner we kept a good tempo."