The 31-year-old newly-installed vice-captain also rejected suggestions that striker Wayne Rooney might be easily provoked into hot-headed retaliation when England play the United States in their opening group C fixture on Saturday (June 12).
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"No I don't think so," he said. "Wayne has matured a lot as a player over the last few years as we all know, so I don't see that one happening."
He added: "Discipline is very important now in the modern game, at all levels of football, but especially at the top level whether it is, for me, playing for Chelsea or for England.
"It is so important to have 11 men on the pitch because small details are so important and when you lose a player it can change anything.
"We have to be aware that you can get a red card for something that is not meant, or a bit stupid, and, in fact, any rash decision can affect the team that way.
"So, it is very important that we concentrate a lot on that. The referees are looking for these kind of incidents because the world is watching them and we have to be extra aware of that."
"We must stay disciplined, but we know that we have to be careful not to overstep the mark," he said.
Beckham's dismissal deprived England of a key player and they lost the match against Argentina on penalties after an exhausting 120-minutes battle to reach the last eight.
Rooney's red card was similarly costly as the remaining ten men struggled through extra-time again before losing on penalties to t
