The Blues were 2-0 winners on Saturday courtesy of two goals from Romelu Lukaku.
Two goals from Romelu Lukaku against his old side saw the Toffees into the semi finals of the competition, the first of which was a wonderful solo effort.
It was an especially pleasing victory for Martinez’s side, who impressed in front of new majority shareholder Farhad Moshiri in his first game at Goodison Park.
And while star man Lukaku impressed Kenwright, it was Martinez he singled out for praise.
“I think we've got to acknowledge Rom's goal though because it was an unbelievable goal wasn't it,” he told the club’s official website.
“[But] you know what I thought today? What a manager. That's what I thought.”
“You can't hide from the fact that there's been the odd kind of criticism this week but he's stood firm and he's just beaten Chelsea with some to spare.”
The win has certainly gone some way to easing some of the pressure that has been rising against Martinez in recent weeks.
Despite playing attractive football, and boasting their best squad in a number of years, they currently sit 12th in the table, a position that is regarded as far below where they should be.
That has seen Martinez coming in for criticism, especially after a poor campaign last year, with many questioning whether the club should move to replace him.
They haven’t though, and securing a trip to Wembley will have done wonders for his approval ratings at Goodison Park.