Did I Call This Correctly?

[ABC Coach]

Team A made a shot and team B quickly inbounded the ball. Team B threw the ball to half court, where one its players was waiting for the pass in his frontcourt. He bobbled the pass and the ball ended up going back into his backcourt without that player ever establishing possession. One of his teammates who was still in the backcourt picked up the loose ball and dribbled it into the frontcourt. I didn't call anything on the play and just let the game continue (the game was a blowout, so no real damage was done if I was wrong). Was this a backcourt violation...or...because no actual possession was made in the frontcourt, did I make the right call? Any help is appreciated.