The Reds missed out on the league title on the final day of the season after being held to a draw by relegated Market Drayton Town.
They then surrendered a 2-0 lead to lose 3-2 at home to Marine in the play-offs.
A club statement said: “Following a disappointing end to an otherwise successful season, on and off the pitch, the board have taken the decision not to renew the contract of Chris Willcock for the 2022/23 season.
“This was a difficult decision as the club narrowly missed out on automatic promotion as league champions and promotion via the playoffs. However, we believe a change in direction will give us the best chance of reaching this target next season.
“The board would like to thank Chris and his family for their hard work and commitment over the past 10 months and wish them every success in his next football venture.
“The search for a replacement begins immediately and we hope to have the new manager in place in good time for the start of the new season.”
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