The new England manager's brief is to improve the fortunes of a side who last reached a major tournament semi-final at Euro 96.
Southgate found himself dealing with a media firestorm last month when it emerged captain Wayne Rooney and other players had stayed up late drinking on a night-off during the international break.
While Southgate is reluctant to impose "Draconian" rules, he says England cannot hope to emulate teams like the all-conquering New Zealand rugby side if their off-pitch behaviour is counter-productive.
"I think if you look at top sports teams, the All Blacks are one of the best examples of teams that have won over the years," he told reporters at Wembley.
"The players are involved in that, because you are giving them ownership and accountability.
"And if they want to be top, top players, which I believe they do, they have got to recognise what are the things that are going to help us achieve that and what are the things that are going to detract from that.
"If we think we are good enough to take on the best in the world without doing everything right along the way, then good luck with that."
Rooney, 31, apologised after he was pictured looking worse for wear as he posed for photographs with people attending a wedding at the England team hotel.
The Manchester United striker branded media coverage of the incident "disgraceful", but Southgate believes it is in the players' interests to keep themselves out of the headlines.
"Where I will be clear is that there is a level of expectation when you are with England," Southgate said. "We talk about pressure and we spend most of our time trying to relieve it.
"So if we put ourselves in positions where we are going to increase that pressure, it is not intelligent."
Southgate, 46, has been appointed England manager on a four-year contract, having previously filled in for four games after Sam Allardyce's premature departure following a newspaper sting.
His brief is to improve the fortunes of a side who last reached a major tournament semi-final at Euro 96, when Southgate was in the team, and who have not won a knockout match since the 2006 World Cup.
Southgate was the only man interviewed for the job, but Football Association chief executive Martin Glenn dismissed suggestions he had been given an easy ride.
"It was reported as a 'fire-side chat', but it was anything but," said Glenn, who flanked Southgate along with FA technical director Dan Ashworth as the new manager was presented to the press.
"It started off with a review of, 'OK, go through the last four games. What have you learnt?' And there was some pretty feisty opinions from the more technical (football) people in the room about some things.
"That was a good example of saying, 'OK, do Gareth's powers of analysis stand up to scrutiny?' Secondly, and as Gareth has said himself, thinking correctly under pressure.
"It's really important for the England team and is important for anyone in what is a high-pressure role. So we had Gareth independently assessed for mental strengths and how he takes decisions."
Southgate begins his full-time tenure with a friendly against Germany in Dortmund on March 22.