England started their World Cup campaign with an encouraging performance in Manaus, but the 2-1 defeat to Italy leaves Roy Hodgson’s men in serious danger of heading home early.
To stop that happening, Sturridge believes England “must” beat Uruguay in Sao Paulo on Thursday.
Sturridge’s Liverpool team-mate Suarez is a doubt for the game because of a knee injury.
He scored 31 goals for Liverpool last season and collected a host of individual awards in the process, but Sturridge wants to see his team-mate line up against him later this week.
“I wish him well and I hope he is fit,” the England striker said.
“We want to face the best Uruguay possible.”
Suarez did not come off the bench in Uruguay’s shock defeat to Costa Rica on Saturday, but the striker has indicated that he will be fit for Thursday’s game at the Itaquerao Stadium.
Suarez sent his Liverpool team-mates in the England camp a text when he suffered the injury to tell them that he would be fit to face them in the Group D match.
But now he has severed all contact with the group, Sturridge revealed.
“I’m not on texting terms (with him),” the former Chelsea striker said. “He’s not asked me for any clues and I won’t be asking for any clues from him.”
Sturridge enjoyed what he termed a “telepathic” and successful partnership with Suarez last season.
But they both experienced huge disappointment two months ago when they led the Premier League, only to let the title slip through their fingers.
They needed West Ham to beat Manchester City on the final day of the season to clinch the trophy – and that did not happen.
Sturridge is therefore wary of England relying on other results to make it through their group and he believes they cannot afford to drop points against Uruguay.
“A draw could be enough (if other results go England’s way), but from what I have learned at Liverpool, you need to get the job done when it’s in your hands because you know it’s best to do it yourselves rather than ask for favours,” he said.
“We know what we have to do and if we lose we are going home.”
England’s players were visibly upset when they filed out of the Arena Amazonia on Saturday night after giving their all in the sweltering jungle heat.
But now they have had time to analyse the performance, they are upbeat about their chances of qualifying for the knockout stages.
“One defeat does not crush spirit,” Sturridge said. “When you lose games it hurts, but you get over it because you have another game to come, another final to come.”
The calls for Wayne Rooney to be dropped may be growing, but they are falling on deaf ears inside the England camp, with Danny Welbeck backing his team-mate to make a difference wherever he is deployed.
England’s attack against Italy was widely and deservedly praised by onlookers, but Rooney’s performance was muted compared to the rest of the front four.
Starting in an unfavoured left role, he provided a fine assist but looked uncomfortable at times, leading some to propose that he should be dropped against Uruguay – a suggestion put to England and Manchester United team-mate Welbeck.
“First and foremost, Wayne Rooney is a class player and I think wherever he is playing on the pitch he can make a massive impact,” the striker said.
“I think all the forward players with England have the flexibility to move in and round, interchange positions.
“Obviously Wayne was on the left in the first game and in the second or third game he could be in a different position.
“Waz is the top all-time scorer for England currently playing, he has got 93 caps and he is very experienced.
“When he is on the pitch, he can make a difference.
“You say he is playing out of position, but he has played there plenty of times for Manchester United as well.”
England fly to Sao Paulo tomorrow. It looks as though Alex Oxlade-Chamberlain will be fit for the game after he stepped up his recovery from a knee injury.
The Arsenal midfielder took part in training at England’s base in Rio on Monday, exchanging passes with his team-mates in the warm-up.