Branded a "golden generation", Gerrard was part of an immensely talented squad that failed to get beyond the quarter-finals of a major tournament under a number of different managers.
The 45-year-old, who won 114 international caps, led Liverpool to the Champions League in 2005.
Manchester United's crop of England stars, including the likes of Rio Ferdinand, Paul Scholes and Wayne Rooney and the Chelsea contingent of Ashley Cole, John Terry and Frank Lampard also enjoyed Premier League and Champions League success at club level.
But Gerrard said those club divisions prevented England from gelling as a team.
"We were all egotistical losers," Gerrard told the Rio Ferdinand Presents podcast, highlighting the camaraderie that now exists between the same players in their punditry careers.
"So why didn't we connect when we were 20, 21, 22, 23? Was it ego? Was it rivalry?
"It was down to the culture within England. We weren't friendly or connected. We weren't a team. We never at any stage became a real good, strong team."
England are still waiting to end their wait since the 1966 World Cup to win a major men's international tournament.
However, they did reach the final of the past two European Championships under Gareth Southgate.
After losing the Euro 2024 final Southgate stood down, with Thomas Tuchel now in charge of England's hopes at next year's World Cup.
"Gareth Southgate is underrated for how he connected with the England team," Gerrard said.
"Because for me, the talent was there (in my time). The players were there. The level of games we were all playing at was there to go and do better than what we did.
"We had a little bit of bad luck with penalties or whatever. We have to take responsibility, but I've got a big frustration when I look back at England that we never did better.
"I think it's a combination of different things, but one of the big things for me was we weren't a team. We were a group of individuals with talent and it never works like that."
Gerrard's own managerial career has stalled after poor spells at Aston Villa and Saudi side Al Ettifaq.
However, he is among the favourites for a return to Glasgow giants Rangers, who he won the Scottish Premiership with in the 2020/21 season.
"There's a part of me that still feels that there's a bit of unfinished business in terms of wanting to go in and face another couple of exciting challenges," the 45-year-old said on getting back into management.
"But I want a certain type of challenge. If in an ideal world they come available, I'll jump at them. If they don't, I won't go back in.
"I want to be at a team that's going to compete to win because I think that suits me better."