Southgate’s side’s preparations for the tournament have been mixed with a 3-0 victory over Bosnia-Herzegovina followed by a disappointing 1-0 defeat by Iceland on Friday.
England start their Euro campaign against Serbia in Gelsenkirchen on Sunday, 16 June before games against Denmark and Slovenia.
“I think about half of the national coaches leave after a tournament – that’s the nature of international football,” said Southgate, who has been linked to Manchester United if they sack Erik ten Hag.
“I’ve been here for almost eight years now and we’ve come close. So I know that you can’t keep standing in front of the public and saying ‘please do a little more’, because at some point people will lose faith in your message.
Asked why he did not sign a new contract before Euro 2024, Southgate said: “The reason is that there would have been more criticism, which would have put more pressure on the team.
“England did that once before with Fabio Capello and there was a big drama before the tournament. It’s better to check yourself after the tournament.”