Claude Puel's men were unable to find their way through a team that stunned Inter Milan with a 2-0 win in their opening group match earlier this month.
The points were shared between the two teams, who sit first and second respectively in the group, with Sparta Prague third and Inter bottom of the standings having lost their first two games.
The Saints should have been leading after the fourth minute from a free kick when the ball was whipped into the box by James Ward-Prowse.
The perfectly-weighted ball found Virgil van Dijk, who simply needed to nod the ball home from four yards out, but he fluffed it and his chance dropped over the crossbar.
It was the best goalscoring opportunity of the first half as neither side posed too much of a threat at either end of the pitch.
Southampton seemed content to sit back and allow Be'er Sheva time on the ball, which could have come at a price as the hosts tried to break the deadlock.
Anthony Nwakaeme tried his luck with a shot from outside the area, but he directed the ball straight at the keeper, and the attacking waves kept coming from Be'er Sheva.
Were it not for a well-timed tackle from Van Dijk, the home team could have been one goal to the good when Mihaly Korhut threaded the ball through to Maor Melikson in the box, but Southampton's defender cut across to thwart the chance.
The Serbian made an instant impact as Southampton saw more of the ball and dominated the closing minutes of the first half, but they could not create a single shot on target in the opening 45 minutes.
After the break, Be'er Sheva started brightly, with Amit Bitton delivering the ball into the box from the right-hand side to find Lucio Maranhao, who could only flick the ball wide of the goal.
The Saints began to find their feet by pegging their opponents back into their own half, and Ward-Prowse produced a strike from 25 yards out after breaking away from his marker, but goalkeeper David Goresh dropped to his right to make the stop.
Be'er Sheva came close to going in front when Nwakaeme played in Melikson, who drilled it low across goal, but the ball trickled inches wide of the back post.
Tadic tried to inspire his teammates as he picked out players numerous times with pin-point passes, but it was not to be as neither team found the back of the net.