Martin Johnson's men beat Georgia 41-10 in Dunedin but, for the second match in succession, they conceded a raft of penalties.
However, as was the case in England's opening 13-9 win over Argentina, poor opposition goal-kicking helped the 2003 champions on the way to victory.
Johnson, in a rare public outburst, warned England that if performances did not improve, players would be making an early return home from the tournament.
"We've been together a long time and the last thing you want is for things to get comfortable," Thompson said.
"Sometimes everyone needs to give each other a little pat on the back or a little boot up the backside and that's what's happening. It's perfect for us.
"It's like a relationship: sometimes you get a little bit stale, don't you? Sometimes you've got have a little bit of an argument and have the old make-up afterward.
"That's what this group of players is all about. Honesty is the best policy, as they say, 'stab you in the belly rather than in the back', that's what we need," Thompson, England's most-capped hooker of all-time, explained.
"In 2003, we had exactly the same thing after the Samoa game when we came close to losing (England won 35-22). We had to move on."
However, Thompson believes England, who have played two, won two as they bid to compete in a third successive World Cup final, are better placed than sides such as Australia, who suffered a shock 15-6 loss to Ireland.
"Sometimes if you are winning ugly and being harsh on yourself, sometimes it's a good place to be," said Thompson, who missed England's run to the 2007 World Cup final after announcing his retirement with a neck injury.
"If you're just scratching through or you're even losing matches, you've got to look at yourself and say 'well, we're not good enough to win this'. But we know we can go and win the next game.
"We're two from two and we're moving forwards."
England face Romania on Saturday, and Thompson, who came across some of the Eastern Europeans' pack during his time in French club rugby, expects a brutal scrum battle against the Pool B outsiders at the Otago Stadium.
"I know a bit about them, especially the hooker (Marius Tincu)," he added. "He's been one of the outstanding players of the tournament so far," former Brive forward Thompson said of the Perpignan front row.
"I thought the Georgians were good and they're big, but I'd say the Romanians are a tougher scrummage."
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