The Everton manager recognised Monk's leadership qualities when he made the centre-back captain during his Swansea tenure.
Monk now finds himself head coach at the Liberty Stadium following Michael Laudrup's sacking earlier this month and the 34-year-old has taken four points from his first two Premier League games.
Swansea beat rivals Cardif City 3-0 in Monk's first game in charge and he now turns his attention to an FA Cup fifth round tie at Goodison Park on Sunday.
He said: "The games are not about managers or where they have been.
"I'll always share magnificent memories of my time at Swansea but the game on Sunday is about the fifth round - a unique opportunity to get into the sixth round.
"Garry Monk was my first big decision as manager, I built a new squad around him. I knew he was the perfect captain.
"It's a nice twist, a nice moment to see him in the dugout on Sunday.
"The Welsh derby can be intense as it gets for a new manager. It was a good start and he's showing that his group is reacting well.
"We expect a very difficult encounter on Sunday."
Martinez has fond memories of the FA Cup, having masterminded Wigan Athletic's shock triumph over Manchester City at Wembley in May.
Everton hammered League One strugglers Stevenage 4-0 in the fourth round, having thrashed Championship promotion-hopefuls QPR by the same scoreline in the previous round.
