Pyke, 24, surprised onlookers when used in a starting role on the right flank in the 1-1 draw against Sunderland on Tuesday, having previously played the role from the bench on the odd occasion.
The striker, signed by Sam Ricketts in 2020, has been unable to lock down a place in Town's starting ranks during his spell at Shrewsbury but was called into action in midweek with Elliott Bennett suspended and Josh Daniels injured.
Cotterill, who was without five senior first-team players on Tuesday, revealed he had wanted to experiment with former Wrexham man Pyke in the position before and was glad to finally have the opportunity.
He said: "Going back to the (Stratford) cup game the other week I actually wanted to play Rekeil as a right wing-back.
"He plays right wing, Elliott (Bennett) is 32 and when we play three games in a week that's a lot for a 32-year-old, it's a lot for a 23-year-old to churn out.
"I didn't like the circumstances that I had to try him on Tuesday but I wanted it a couple of weeks ago and didn't get the opportunity. Now I've had it, it just adds a little bit more flexibility to the squad."
Even without two centre-halves, Cotterill retained the back three which has become an ever-present in Town's game this season.
He switched the versatile Luke Leahy, who was captain for the night, in the middle of the trio, flanked by the excellent Matt Pennington and George Nurse as Ethan Ebanks-Landell and Aaron Pierre missed out through injury.
Cotterill has championed Leahy's flexibility and utilised against the Black Cats and his role in a back three was something he trialled in pre-season in July.
"That back three played at Exeter in pre-season – so I knew what they could do and thought that's the way we'll go, thankfully it paid off for us and the boys because my God don't they deserve it?" Cotterill added.
"And the fans were brilliant, brilliant for the boys, we need them like that all the time, the boys need them like that, thank you to them."
On the prospect of his two stoppers returning to availability for Saturday's visit of Charlton, the boss added: "Pierre started the warm-up (on Tuesday), so obviously he can't be that bad.
"Ebanks-Landell probably has been carrying a little nick of a hamstring for a week-ish. I think he hurt it at the end of Cheltenham, but he came in Sunday for treatment and is in on Wednesday again.
"I don't quite know how bad it is, when he'll be back. Elliott will be available, Josh Daniels is still a little bit away. We'll see what we've got, good job there's a bit of flexibility in them."