Southgate's team will become the first Three Lions outfit to lift a European Championship if they win at Wembley.
"When we started, three or four years ago we had people throwing paper aeroplanes, they weren't behind the team and there was an apathy," he said.
"Now the energy in the stadium is fantastic. That is so important."
England have not won a major men's tournament since their World Cup triumph in 1966.
Southgate was asked about the role fans can play in the showcase final, which will be watched by 60,000 at the national stadium - and millions more in homes and in pubs.
"The players need to feel that warmth and support. It has definitely helped inspire us," he added.
"Over the last four years the players have knocked down so many barriers, they've come through so many different challenges."
Southgate also urged supporters to show respect for the Italian national anthem before the final, which is live on BBC One.
A section of fans booed the German national anthem before England's 2-0 win in the last 16.
"It's important that our fans always respect the opposition," added Southgate.
"We know that in actual fact, when we play abroad and fans boo our anthem, it probably inspires us even more. We should be respectful."
Team news - Foden 'definitely doubtful'
One absentee from England's training pitch on Saturday was midfielder Phil Foden, who suffered a minor knock on Friday.
The Manchester City player started their first two group games and came on as a substitute in the semi-final.
"He's definitely doubtful although it's not something serious. It's just whether it will keep him out of this particular game," said Southgate.
Italy are without left-back Leonardo Spinazzola, who suffered a ruptured Achilles tendon in the quarter-final. Boss Roberto Mancini must decide whether to play Chelsea's Emerson Palmieri, who started in the last-four win over Spain, or make another alteration to a defence which was previously settled.
The Azzurri transformed under Mancini
Former Manchester City boss Mancini has transformed Italy since taking charge following the disappointment of their failure to reach the 2018 World Cup.
The Azzurri went into Euro 2020 with the best form of any nation and they have extended their national record further with the semi-final victory over Spain a 33rd match unbeaten - a run stretching back to September 2018.
"This is possibly one of the highlights of my career," said Mancini.
"I had the opportunity to play for the Under-21 side, the senior side, yet we weren't able to win the under-21 Euros or the 1990 World Cup.
"It's a very important moment for me because I represent Italy so I really hope I can enjoy the experience that I didn't enjoy during my playing career."
Four-time world champions Italy are seeking a second European title - and first since 1968.
England to win on penalties?
BBC Sport football expert Mark Lawrenson
This is a fitting finale to an extremely good tournament, and it will be a very close game. Italy have been the best team at Euro 2020, but England are not far behind them.
I can see it turning it into a tactical battle - and it is very hard to call it.
'England are favourites'
Simon Gleave, head of sports analysis, Gracenote
"Italy are ranked third in the world by Gracenote's world football ranking and would be favourites if this match was being played on neutral ground.
"However, data tells us that finals do not have the same level of home advantage as other matches in the tournament so England's edge will be lessened on Sunday.
"Even so, England are still favourites on Sunday evening with a 53.5% chance of becoming European Champions for the first time."
* England have won just two of their past 14 meetings with Italy in all competitions, a 2-0 success in June 1997 and 2-1 in August 2013 - both in friendly matches.
* Italy have never lost against England at a major tournament, winning 1-0 at Euro 1980, 2-1 at both the 1990 and 2014 World Cups, and drawing 0-0 before winning on penalties at Euro 2012.
* This is Italy's 10th major tournament final with only Germany (14) having played in more among European nations. Italy won the European Championship in 1968, but have lost their subsequent two final appearances in the competition (2000 and 2012).
* Italy's Roberto Mancini will be just the second manager to have won the English top-flight title and take charge of a European nation in a major tournament final. Sir Alf Ramsey won the old First Division title with Ipswich in 1962 and 1966 World Cup with England.
* Italy have had 12 shots and scored three goals as a result of a high turnover (open-play sequences beginning 40m or less from an opponent's goalline) at Euro 2020, more than any other side.
* England are the 13th different nation to feature in a European Championship final. Just three of the previous 12 lost their first-ever final in the competition.
* England have won 15 of their past 17 matches at Wembley in all competitions (D1 L1), scoring 46 goals and conceding just five in this run.
* England's 2-1 win over Denmark in the semi-final was their eighth win in a major tournament match under Gareth Southgate, moving him level with Ramsey for joint-most victories by an England manager across the two competitions.
* Harry Kane has been directly involved in 28 goals in his past 27 appearances for England in all competitions (19 goals, 9 assists). One more goal will see him become England's outright highest goalscorer at major tournaments with 11 - a record he currently shares on 10 with Gary Lineker.