The club has confirmed that first-team coach Richard Keogh will take over as interim head coach as the side faces Cambridge United on Saturday.
Simon Sadler spoke about the decision that was tough for him to make.
"Despite his best efforts over the past 12 months, there have been a number of disappointing results and performances which means that a change is needed to give the club every possible chance of competing at the top end of the division this season.”
"I will always be thankful for Neil's wonderful efforts in guiding the club to promotion to the Championship in 2021, and then comfortably keeping us in the division the following season.
"I and all at the club wish Neil and (assistant head coach) Mike (Garrity) the very best for the future."
Critchley led the side to promotion to the Championship two years previously so this sacking came as a shock to many who believed the 45 year old was the man for the job.