Sturrock watched in dismay as a struggling Saints side outplayed his play-off chasing team in a 0-0 draw at St Mary's.
Sturrock said: "I think we were too complacent tonight and at least 30% below par in the first half.
"I had to have strong words with my players at the break and at least they came out after half-time and competed, because they certainly weren't doing that in the first half.
"We were second to every ball in the first 45 minutes and it just wasn't good enough.
"I expect better of my players because they have been performing well recently but they let themselves down tonight.
"Overall I think a draw was a fair result but we came into this game expecting to win and maybe the players thought the three points would be easy, but football is rarely like that."
Southampton's top scorer David McGoldrick missed the best chance of the game just after the break.
McGoldrick, who has scored five league goals this term, was sent clean through by a lovely ball from Adam Lallana.
He rounded Plymouth goalkeeper Romain Larrieu before shooting but left-back Chris Barker did well to clear off the line.
Plymouth were toothless until top scorer Paul Gallagher came off the bench 11 minutes into the second half.
The striker, who is on loan from Blackburn, made an immediate impression when he fired just over the bar from 20 yards with his first touch.
Veteran defender Chris 
Southampton boss Jan Poortvliet was disappointed with the way his side tried to walk the ball into the back of the net instead of shooting.
He said: "I think the players were tired after playing two games in four days and the 2-1 victory at Reading took a lot out of them, but that is no excuse for trying to walk the ball into the back of the net.
"They are young but they must learn how to take opportunities when they are presented to them.
"I thought we were the better side and we created a lot of problems for Plymouth but we did not take our opportunities when they came to us."