The influential midfielder played a key role in the club reaching last season’s promotion final, but will depart after just one campaign at the Jakemans Community Stadium.
In a statement posted on social media, Byrne suggested he was keen to remain with the Pilgrims.
He wrote: “Well looks like my time at Boston United is up after just one year.
"Loved my time at the club and absolutely gutted I won’t be there next season. Honestly didn’t see myself anywhere else for the new season.
"Felt like we had unfinished business.”
Byrne continued: “I was disappointed with the communication from the club having only heard from them last Monday for the first time, with an offer that I didn’t felt reflect(ed) my contributions last year and was told today there was no improvement on it at all so unfortunately we couldn’t come to an agreement.”
The Irishman also thanked the Pilgrims fans.
He added: “Just wanted to thank the fans who have been outstanding this year and proper welcomed me into the club.”
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