EMB-145 Captain reported a go-around due to a 'Ground Conflict; Critical' warning; which was caused by improper automation sequencing. The flight remained clear of terrain and complied with ATC instructions; and circled back around to land safely.

Narrative

While on visual approach to RWY XX in ZZZ; we were given vectors for sequence to follow a cirrus on base leg; 3 miles in trail of the other aircraft. Originally Approach had assigned speed 180 or greater to the FAF; and when getting switched to tower were told to slow to lowest practical airspeed; with which we complied. The other aircraft failed to exit the runway in time and tower instructed us to go around. During the go-around; we received 'TERRAIN; TOO LOW' GPWS aural warning. In hindsight; we believe it was probably due to the aircraft not switching over to GA (Go Around) mode when FO/PF hit the go-around buttons. I do not recall seeing GA mode on the PFD (Primary Flight Display); and did not recognize the aural warning as being associated with not being in Go-around mode until after further consideration. We remained clear of terrain and complied with ATC instructions; and circled back around to land safely.Cause: Pilots will remain vigilant to ensure proper sequencing to GA mode when pressing the go- around buttons during a go-around to avoid future GPWS events.Suggestions: ATC controllers should communicate with each other better as far as sequencing aircraft arrivals to avoid unnecessary go-arounds. It would have been better if they had asked the cirrus to extend downwind and let us land first. It seemed like Approach control planned to keep us fast to sequence us before the other aircraft; and the tower controller had a different plan; sequencing a slower moving aircraft in front of a faster moving aircraft with 3 miles spacing. Pilots will remain vigilant to ensure the aircraft actually switches into GA mode when pressing the go-around buttons to avoid future GPWS warnings.