A catalogue of near-misses started as early as the first minute and in a dominant 20-minute spell at the start of the second half, Robbie Keane (three times), Teddy Sheringham (twice) and Ledley King were either denied by the excellent Antti Niemi or just failed to hit the target.
Then the sucker punch as in-form James Beattie grabbed all three points for the Saints with eight minutes remaining by drilling home only his second sight at goal all game.
"It's very frustrating," admitted a very disappointed Glenn at St Mary's. "In the last two games we should have had at least four points but we've ended up with nothing.
"In fact, we've played well enough to have possibly won both games.
"Certainly today I thought we were the better team but a clinical finish was the difference between the two teams.
"I've seen them here before and they put you under a lot of pressure, lots of corners and throw-ins but we equipped ourselves well on that front and passed the ball. Now we've got to become more clinical ourselves to finish things off.
"There were a lot of possibilities and we created a lot of good positions, like we did at Newcastle.
"At the moment it's just not going our way but we have to believe in ourselves and if we keep playing like that we'll win football matches, no doubt about it."
Glenn Hoddle was left to reflect again on missed chances after a frustrating defeat against Southampton on New Year's Day.