"There are a lot of experienced players still looking for clubs, which shows you how difficult it is," McAllister told BBC Radio Shropshire.
"I hope I can show what I can do to get back up the leagues with Shrewsbury."
McAllister, who signed a two-year deal with Town, added: "No-one ever wants to get released from a club.
It's started well, so I'm happy to be here
Sean McAllister
"I had seven years at Wednesday and had settled in really well there.
"But I have no hard feelings - it was just a new manager coming in and wanting his own players.
"I was out of contract and was released. Shrewsbury showed their interest in me, and that they have very high ambitions for the club - which is exactly what I wanted."
Shrewsbury are currently top of League Two and McAllister continued: "It's started well, so I'm happy to be here."
McAllister, 23, joined the Wednesday Academy from Bolton in 2006, when he was named their Young Player of the Year.
He made 68 first-team appearances but was loaned to Mansfield and Bury before his release.
Source: BBC Sport
Source: BBC Sport