"After an open and honest meeting last week we unfortunately failed to agree terms," said Boro director Lee Thorn.
"Liam's worked extremely hard to bring in players and has developed a strong mentality throughout the club. He has carried out his role professionally."
Daish's exit was revealed following Boro's final-day 5-3 defeat at Chester.
Boro won just eight times in 38 games in his seven months in charge, the former Ebbsfleet boss having taken over after Brian Reid was sacked on 8 September.
Ex-Birmingham City centre-half Daish will step down after his return to St Andrew's on Thursday, when he is due to lead Boro out in the Birmingham Senior Cup final against his old club.
"It was concluded that the BSC final at St Andrew's on Thursday would be his last game," added Thorn.
Boro are now looking for their fifth manager in the 13 months since Kevin Wilkin, now available again following his sacking by Wrexham, left Liberty Way for the Racecourse Ground in March 2014.
Caretaker boss Mark Noon took control for five games, none of which Boro won before Reid came in until the end of last season.
But when they managed just one win from their first seven games this season, he was sacked but the pattern had already been set for what proved to be a relegation campaign.
Nuneaton Town are to part company with manager Liam Daish after failing to agree terms for him to continue at the relegated Conference club next season.