Sturridge took the place of Roberto Firmino in Liverpool's attack at St James's Park, but was guilty of spurning one of the visitors' best chances in the match when he directed a weak effort at Newcastle goalkeeper Rob Elliott after a wayward clearance fell to him.
Philippe Coutinho's long-range strike at the half-hour mark was cancelled out by Joselu nine minutes later on Tyneside, leaving Liverpool seven points adrift of league leaders Manchester City.
Souness said Sturridge was "off the pace" and warned that it could be a month or more before he is given another opportunity in the first team by manager Jurgen Klopp.
"He didn't take it [his chance]," the former Liverpool midfielder told Sky Sports.
"There was no cuteness in his game that you normally associate with him. I thought he looked laboured, he looked off the pace and I don't think he can train and prepare properly.
"It might be a month or another six weeks before Jurgen Klopp goes with him again. I thought he was so disappointing today.
"If everything is right with Sturridge, he is one of the first names on the team-sheet but looking at him today, he was miles away."
Former Reds defender Jamie Carragher agreed with Souness's assessment, saying Sturridge was no longer the player that terrorised defences alongside Luis Suarez at Anfield three years ago.
"Because he doesn't play much now, whenever we talk about Sturridge we keep going back to that season when Liverpool nearly won the league – he was devastating with Luis Suarez," the centre-back said.
"I don't think that player is there now, whether that's due to injuries or not playing enough."