Sturrock believes Walton's dismissal for kicking out at Barnsley midfielder Anderson De Silva shortly before half-time "cost us dear".
Walton took exception to De Silva's firm challenge and lashed out in front of referee Dean Whitestone, who was left with no choice other than to brandish a red card.
Sturrock said: "You can train football teams, you can shape football teams, you can put them out and give them a gameplan.
"But when somebody does what he did today, all of a sudden the gameplan goes out the window.
"I'm proud of my players to be fair. Second half we came out and gave it a go.
"It's hard enough winning football matches in this league with 11 men without having to play with 10, but to be fair they responded in the right way."
De Silva's deflected 38th-minute header - later claimed by team-mate Jon Macken - and Jamal Campbell-Ryce's last-minute penalty clinched Barnsley their first Coca-Cola Championship win in five matches.
Plymouth's 10 men worked tirelessly after the break to restrict Barnsley mainly to half-chances, but defeat has left Sturrock's side without a league win in their last six games.
Sturrock added: "We're a hard-working team with a good work ethic, but they weren't given the opportunity today because of someone's stupidity.
"I don't think Walts is in the right frame of mind (to apologise). He did the right thing and kept very, very quiet.
"Him and I are having a conversation on Monday morning about the whole scenario.
"There's no point me getting excited about it because things get taken out of context.
"So the metaphorical belt will be brought out on Monday and we'll see where we go from there.
"As far as the rest of the players are concerned he let them down and I'm sure one or two will make sure he knows that."
Barnsley boss Simon Davey wore the smile of a manager whose side had just ended a damaging winless run, but he conceded the Tykes had made hard work of it.
Davey, who also confirmed De Silva's header was deflected in off the top of Macken's head said: "It was hard-earned. Plymouth made it hard for us, especially when they went to 10 men.
"We deserved it. We could have finished the game 10 times over, I think Anderson could have had double figures today.
"He didn't even get the goal he thought he had, it hit Jon Macken's head, so that's Jon Macken's goal.
"We created chances, we passed the ball well, we could have passed it quicker in the first half, but we got three points."
Davey added: "It's been a problem that we've not scored enough goals this season. We've got two today and could have had 22.
"We just need to learn to finish games off."