Unsworth was shown the red card by referee Eddie Wolstenholme following a scuffle with the Dane during Everton's defeat by Chelsea at Goodison Park.
But Gronkjaer protested against the decision at the time and has since publicly defended Unsworth, who saw red for violent conduct.
The Toffees have appealed against the dismissal of the former England defender, but the FA are still waiting to study Wolstenholme's report.
Unsworth told the club's official website: "I'd like to take this opportunity to thank Jesper Gronkjaer for what he said after the game."