The former midfielder was a key member of Bobby Robson's team which reached the semi-finals in Italy before losing on penalties to eventual champions West Germany.
England have won the World Cup just once, on home soil 60 years ago, and the only time they have reached the semi-finals since 1990 was when Gareth Southgate's side made it through to the last four in 2018.
"You want 11 captains on the pitch and when you are playing in a game like that, at a World Cup, you cannot afford to carry anyone," Gascoigne told ITV.
"Everyone has to be on the ball and the team spirit is important.
"The players that didn't play, they were right behind the team, so our team spirit was unbelievable.
"The most important thing is team spirit because that goes a long way."
Thomas Tuchel's men face Costa Rica in their final friendly on Wednesday before a Group L opener against Croatia in Dallas on June 17.
When asked what he would say to the current squad, the 59-year-old Gascoigne added: "Enjoy it. Because you just never know it could be your last World Cup."
FIFA World Cup 2026
The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
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Gascoigne famously burst into tears after being booked in the 1990 semi-final meaning he would have been suspended from the final had England qualified.
His life has been blighted by addiction problems but Gascoigne, speaking following the publication of his new autobiography, said: "Everything's going well for us. It's probably the happiest I've been in about five years, definitely, you know."
Turning to his autobiography, he said : "A lot of people have come up (to me) and said they've read it and (it's) saved their life.
"If that book can save one person's life, then I've done my job," with Gascoigne joking: "I think I should read it myself, you know! Do myself a favour."
He added: "Every morning, I don't think about tomorrow because that's another day. I just try to keep it in the day, keep it simple. Some days I find it hard."