Sparrow signed for Crawley during the January transfer window until the end of the season and made 21 appearances including 17 starts and scored three goals.
Barker said: "We have been talking to Matt for a while and at the outset we agreed a time frame for the discussions so everyone knew where they stood.
"We have reached that time and unfortunately we haven't been able to reach an agreement so Matt is moving on.
"I would like to thank him for his services since he came to the club. He is a model professional and we wish him all the best for his future career."
Sparrow was a target for Brian Laws when he returned to the club earlier this year, but the former fans favourite opted to stay down south after his time at Brighton came to an end.