Tadic at least injected some much needed creativity into the Saints’ attack, his teasing second half cross narrowly evading Shane Long’s head.
James Ward-Prowse finally mustered the visitors’ first shot on target ten minutes after the break when his long-ranger was beaten away by home goalkeeper David Goresh.
But it was Beer Sheva who nearly nicked the win late on with captain Maor Melikson arrowing a shot across goal and Fraser Forester acrobatically keeping out substitute Ovidiu Hoban’s volley.
Southampton: (4-1-2-1-2) Forster; Martina, Yoshida, Van Dijk, Targett; Romeu; Ward-Prowse, Clasie; Hesketh (Tadic, 35); Long, Redmond (Hojbjerg, 85).
Subs unused: McCarthy, Cedric, Reed, Stephens, Olomala
Hapoel Beer Sheva: (3-5-2) Goresh; Taha, Tzedek, Vitor; Bitton, Radi (Hoban, 80), Ogu, Melikson (Buzaglo, 70), Korhut; Lucio (Sahar, 63), Nwakaeme.
Subs unused: Haimov, Shabtai, Broun, Ohayon,
Referee: Stefan Johannesson (Sweden)