Brentford ended a run of three straight defeats after beating fellow strugglers Rotherham by two goals to one.
Alan Judge's excellent volley gave the Bees the lead after 67 seconds but Joe Mattock cancelled it out just after half-time.
The Irishman, though, scored the winner soon after when he headed home Jake Bidwell's cross.
Carsley was delighted with Judge's efforts and wants him to maintain it if he is to win his first Ireland cap.
He said: “I spoke to Judgey. He's been away with the international team so he's got to get used to performing at an elite level.
“An elite level for international footballers is the Premier League, not the Championship. He should be doing that.
“That's not surprised me today that he's done that. He's competing with players in the Premier League who are top performers.
“He needs to get on that level and he's got everything in his locker to get on it."