The former Crystal Palace and Everton boss feels he should still be in charge of England and, in a BBC documentary to be aired on Sunday, said: "Jealous is what I feel".
"We ask people to pay a lot of money to watch football". We want to take this tournament head on,"goal.com quoted the England captain, as saying".
"We just didn't know what to do to get back in the game when we were behind because we just hadn't planned for it".
Ever since England won the World Cup in 1966 and thus set unrealistically high expectations for every squad that proceeded them, the relationship between the media and the England team has grown increasingly toxic.
Southgate confirmed there were no major injury concerns, but would assess Manchester United forward Rashford ahead of the first scheduled open training session on Wednesday.
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Donegan penned the song in 1965 as the official tune to go along with the Football Association's mascot for the tournament.
Southgate prefers a more measured view, focusing on the way the Three Lions go about their work rather than predicting the final outcome.
"We're pleased with how preparation has gone up until now, we fly out tomorrow so it'll be good to get on with it now", said Southgate.
Asked to sum up his own feelings about coaching his country on the biggest stage of all, he added: "I'm a very proud Englishman and I've said before that to play for my country was my only goal as a kid".
The absence of Italy, Netherlands, Republic of Ireland and Chile, who were backed by 13,000 fans during last year's Confederations Cup, has raised the prospect of some games at the World Cup being played to smaller crowds than originally anticipated. Hotels.com will also engage directly with Spurs fans to inspire them to enjoy their leisure time throughout the year.