Defender James Collins missed the best chance of the game for West Ham at St Mary's on Sunday, while Pablo Osvaldo and Rickie Lambert failed to make the most of opportunities for the hosts.
Former Saints star Le Tissier reckons the Hammers could do with Petric getting up to full fitness as soon as possible.
"West Ham need Petric fit quite quickly," he told Sky Sports.
"[West Ham boss] Sam Allardyce said before the game he probably needs four or five weeks of training and they're going to try and squeeze that into a couple of weeks to get him back as soon as they possibly can.
"They need somebody up there who is going to give them a cutting edge because, as we saw today, they don't create too many chances and unfortunately the one they did create fell to a centre-back and it was a centre-back's finish."
At the other end, Le Tissier felt his former side carved out enough openings to deserve the spoils, but questioned whether summer recruit Osvaldo has in fact compromised Saints' successful pattern of play, which reaped rewards last season.
"When you look at the balance of play, the balance of chances created, if Southampton had nicked that game 1-0 it wouldn't have been unfair," he said.
"Artur Boruc didn't have a save to make after the seventh minute from Mohamed Diame's shot so, from that point of view, Southampton maybe edged it. But you can't deny West Ham defended pretty well, made it difficult and fair play to them they take away a point.
"However, it seems Southampton have almost made a problem for themselves with Osvaldo.
"Southampton had a shape and system of play before Osvaldo turned up that was working pretty well and since he came into the side, for the past two games, they've altered the formation a little and not managed to score.
"It's maybe disrupted things a little bit - but hopefully that's just for the short term. There were some nice flicks from him today, some good positive play but the disappointing thing was his missed chance in the first half.
"It was a gilt-edged chance to get off the mark for the club and he wasn't able to take it."