Virgil van Dijk's late equaliser was not enough to secure Southampton's passage to the Europa League last 32 as Hapoel Be'er Sheva held on to a 1-1 draw at St Mary's to progress from Group K.
The two sides went into the match level on seven points and their previous 0-0 stalemate in Israel meant Saints either needed another goalless draw or a victory to progress, but Maor Buzaglo's opener 12 minutes from time ultimately gave the hosts too much to do despite Van Dijk's stoppage-time leveller.
Both teams contributed to an open first half which Southampton just edged, with Nathan Redmond particularly prominent on the left flank.
Clear-cut opportunities were scarce at either end, though, with Van Dijk's second-half header the closest either team came to breaking the deadlock until the latter stages.
Hapoel looked devoid of ideas and craft in what was a rather tepid second period, but an Oriol Romeu error presented the away side with a chance that Buzaglo capitalised upon with a fine effort.
Van Dijk restored parity in the 91st minute, but it was too little, too late as Hapoel held on to the draw to book a place in the knockout phase at their hosts' expense.
The fact the two sides were battling it out for the second qualification spot created an almost-sudden death nature to proceedings, leading to an entertaining, end-to-end first half.
Saints shaded things early on, but Hapoel created the first real chance 19 minutes in, Anthony Nwakaeme's cross finding Buzaglo at the far post and he smashed over from a tight angle.
Southampton should have taken the lead when Redmond raced forward and crossed, but Romeu could not get over the ball and his header ended up going behind him.
The hosts tested Hapoel goalkeeper David Goresh for the first time eight minutes before the break – Redmond again a central figure as he darted in from the left and saw his rasping drive palmed away acrobatically.
Although Saints needed a last-ditch Maya Yoshida tackle to halt Ben Sahar inside the area early in the second half, Hapoel's approach was rather more withdrawn after the break.
Claude Puel's men appeared to have significantly more control over proceedings and troubled the visitors in the 55th minute, Ryan Bertrand's teasing left-wing delivery forcing Miguel Vitor to prod the ball just wide of his own goal as Shane Long lurked.
Hapoel's second-half struggles continued and they almost found themselves behind with 21 minutes to go, as Van Dijk met Steven Davis' corner ahead of Goresh and nodded just wide of the empty goal.
And Be'er Sheva made the most of that reprieve when Romeu was caught in possession just outside his own area and the ball was worked right to Buzaglo, who fired across goal and into the bottom-left corner from 20 yards.
Van Dijk gave Saints a lifeline in the first minute of stoppage time as his controlled 10-yard finish deflected past Goresh, but Yoshida was unable to take a chance to secure the win moments later and Hapoel dug in for the final seconds to advance behind Sparta Prague.
