Watford's draw at Blackpool meant that Wolves missed out on a top-six finish on goal difference.
The Hornets' point meant Wolves needed to win by three clear goals to force their way into the play-offs. But goals have proved hard to come by for Wolves all season and it once again it proved their undoing as they failed to turn a dominant display into a commanding win.
All they had to show for their efforts was a strike from Nigeria international Olofinjana three minutes from time. He powered clear from midfield and chipped the ball over the advancing Plymouth goalkeeper Luke McCormick.
Defensively, Plymouth had been superb with Krisztian Timar and Russell Anderson outstanding at the heart of their back line.
It was no surprise that their resistance was finally broken ten minutes after Timar had been stretchered off following a challenge by the Wolves left-back George Elokobi.
Wolves should really have taken a commanding lead into half-time on the basis of the possession they enjoyed but they missed two gilt-edged chances.
Plymouth, who only threatened once when Gary Sawyer fired into the side-netting after a powerful run, were let off by Michael Kightly in the 18th minute.
A cross from Matt Jarvis was helped on by Andy Keogh into the path of Kightly, but the England Under-21 international sliced his drive wide.
Keogh was equally off-key in front of goal on the stroke of half-time when he was picked out by a centre from Olofinjana only to miss the ball completely at the near post.
They could have been costly misses as Plymouth enjoyed their best spell of the game at the start of the second half.
Jamie Mackie shot wide in the 54th minute and then, 60 seconds later, he should have done better with a header that he directed straight at goalkeeper Wayne Hennessey.
Kightly then wasted another excellent chance after being teed up by Sylvan Ebanks-Blake.
Olofinjana finally made Wolves' pressure pay with three minutes remaining, but it was too little for Mick McCarthy's side to take their campaign into extra time.