England manager Gareth Southgate said it is an "embarrassment" for the national team to play without fans and called for better behaviour at stadiums after a string of pitch invasions marred the end of the domestic season.

England were ordered to play their next two home games in UEFA competition without supporters present after disturbances during their Euro 2020 final last year. 

Southgate's side host Italy in the Nations League on June 11, in a rematch of that final, behind closed doors. The ban on fans attending the second game has been suspended for a probationary period of two years.

"We're on a yellow card and we've got the embarrassment now of playing behind closed doors at home," Southgate told reporters.

"We still want to host events. We've got a women's Euros here this summer which should be a brilliant experience for everybody ... We're talking about something that could cost us the chance of doing those sorts of things ..."

Several pitch invasions occurred in English football over the last few weeks, with Aston Villa's Robin Olsen, Sheffield United's Billy Sharp and Crystal Palace manager Patrick Vieira being involved in on-field incidents with fans.

"When it's in our environment, we have to do all we can to make sure it doesn't happen," Southgate said. "It's a wider problem, a reflection of where we are as a country.

"We don't want to go back to fences up (at stadiums) and the type of environment that created. At various times in my lifetime, football has become a vehicle for people who want a fight and want to do whatever.

"We don't want to head back there."

England open their Nations League A Group 3 campaign against Hungary on June 4 in Budapest, a match that will also be played without fans due to incidents during Hungary's Euro 2020 games.

England then have a trip to face Germany three days later.