Johnson has spent much of the last week talking about the negative aspects of his side's 41-10 victory over Georgia, particularly the sloppy final quarter.
Having seen South Africa drive all the way to the whistle in thrashing Namibia 87-0, he is demanding the same focus from his players in their Pool B game.
"We need to be relentless. We need to come out and play to a certain level to give ourselves the best chance," he told a news conference after the players trained at Otago Stadium.
"We've got to set our sights high, higher than they were last week. You can say it any number of ways but we've got to play a lot better.
"We scored six tries but I'd be happier if we played a lot better and scored three or four."
Victory should be a formality against Romania, who are resting several leading players ahead of their game against Georgia next Wednesday, so Johnson and his coaching staff will be looking for his team to follow the much-trumpeted "processes" demanded of them.
Johnson knows that Scotland, who they face in their final Pool B game next Saturday, and their subsequent knockout phase opponents will provide a much tougher test.
England are virtually at full strength with only injured duo Matt Stevens and Nick Easter, as well as suspended lock Courtney Lawes, unavailable and Johnson is happy that by the end of Saturday's game all the squad will have had a taste of the action.
"If they'd come off a long season it may be different, but they've not got a lot of game time so you want to get everybody on the field," he said.
"If you're going to come in and play one of the biggest games of your career, you need a little bit of background in terms of actually being on the field.
"People talk about knowing your best team but we know what our choices are and what we can pick and how that would affect the team and we're very comfortable with that."
Easter's back problem is improving and England will make a decision by the end of the weekend on whether to add Thomas Waldrom to the squad after he arrived in Dunedin this week as cover - meaning he cannot stay, travel or train with the squad.
Johnson still has the option of calling up someone else to replace prop Andrew Sheridan, who has gone home for shoulder surgery. England came out with five props in the group so may not make a like-for-like replacement.
Johnson said he was hedging his bets and waiting to see if any new injuries come out of Saturday's game.
Captain Lewis Moody says he has fully recovered from the knee problem that dogged him all year and kept him out of the opening win over Argentina.
"Getting on the pitch finally was the culmination of a lot of work," said the flanker, who returned to lead the team against Georgia last Sunday. "It was frustrating but I got through that game with no issues so it's all done and dusted now and I'm really excited to be going out there."