Abbott signed Madden for an undisclosed fee from Irish side Bohemians in 2011, but the 23-year-old made only eight starts for the Cumbrians and 28 substitute appearances before joining Yeovil on loan last October.
Madden scored nine goals in 16 games for Yeovil before making his move to Huish Park permanent in January and has gone on to notch 21 goals in 32 matches this season, including one at former club Carlisle in last weekend's 3-3 draw.
"Paddy Madden was an absolute credit (on Saturday)," Abbott told Carlisle's official website. "His time here was frustrating, but he has moved on and good luck to the kid.
"He showed a huge amount of respect with the way he conducted himself and we wish him all the best.
"He's a player playing with confidence and if he goes on to make the career he wants to make for himself then you have to be big enough and bold enough to hold your hands up and say you maybe got that one wrong.
"It happens, it's football, and some players do better at other clubs for a number for reasons.
"All I can say is that it didn't happen for him here and give a genuine good luck wish to the lad."