Keith Briggs has left Shrewsbury after boss Gary Peters decided not to offer him a contract.
Briggs joined the Shrews on non-contract terms after training with the club for a fortnight.
He scored on his debut in the 3-1 defeat to Hereford but Peters has decided against handing him a deal because he felt it would not sufficiently improve his side.
He told the club's official website: "Keith is a good lad, a steady type who knows and understands the game and is a very likeable character.
"Unfortunately I felt that he didn't make that difference. He would have been a good steady player but wouldn't make us that much better.
"With that in mind I thought it was pointless to give him a contract because if I did it would be stopping players who probably need the games to improve."