Following a return from injury, the defender started the losses to Southend United and Cheltenham Town, but was substituted after 70 minutes in both.
With James Clarke returning to fitness and Zak Jules moving over to left-back, Cockerill-Mollett was left out of the squad for the visit to Newport and Clarke is now demanding more from him.
“I thought Jules was outstanding at left-back,” Clarke said.
“He’s come in for Cockerill-Mollett who has had a bad couple of games in my opinion and he’s done really well.
“Clarke has come back in, that experience, the captain. He’s horrible to play against and he doesn’t leave attackers alone for a minute.”
When asked if Cockerill-Mollett’s absence was due to injury, Clarke added: “He’s not injured I just thought the last couple of games he hasn’t got to the standards that he set himself.
“He’s a great lad, a great worker and these young lads have to come out the team.
“He’s not that young now, as well, so he needs to start learning a little bit quicker.
“That’s what he’ll do and we’ll rally around him.
“It’s a squad game, there’s loads of games and they’ll be other opportunities for those players and they have to make sure they take those opportunities.
“I can’t keep rolling out players if they’re not performing so we have to look at different angles.”