Alcock had been named in the starting XI but was replaced by Matty Blair at short notice after feeling the effects of a groin problem just minutes before kick off.
The full back suffered with the injury in training during the week but it was thought he would be able to play.
Alcock spoke up as the teams returned to the dressing room following the warm-up and was replaced by Blair, who played well during the goalless draw at Roots Hall.
"We've had to change the team, the personnel, all the time because of injury recently," boss Darren Ferguson said.
"Again, we had to do it before the start of the game, at ten to three.
"We had to change the team with Craig Alcock feeling his groin. But Matty Blair came in and did tremendously well.
"We knew the situation before. We knew on Thursday and Friday and had a conversation with him but he felt he'd be fine.
"We said we'd see how it was.
"To be fair, Blair warmed up with the starting team and Craig came in quite late to say he wasn't right.
"As a player, it's difficult to do that but at least he was honest because if he'd played and done it worse he could have been out for a lot longer.
"And I thought Blairy came in and did very well which will not hurt his confidence.
"I thought the back four did fine against a team, apart from last week, that have been one of the form teams in the league, beating Wigan here, beating Portsmouth here comfortably."
Snap report: Southend 0 Rovers 0