Nigeria international, Kelechi Iheanacho’s second-half goal proved decisive for the Foxes, whose last major final of any description came in 2000, when they lifted the League Cup.
“That is what this game is about, creating a memory,” said Rodgers, who is yet to win major silverware in English football, but won seven trophies in less than three years as manager of Celtic.
“I have been made aware since I’ve been at Leicester how important this cup is for the supporters.
“We have the chance to create history. When we arrived here, that was the ambition. From a football perspective we wanted to be able to compete and we have been able to do that. Now we have a trophy to genuinely go for.”
Iheanacho, who benefited from Jamie Vardy’s fine work to score at the second attempt 10 minutes after the interval, added: “It is a dream come true. I watched the FA Cup when I was little and now I get the chance to play in the final.
“I think the FA Cup loves me and I love the FA Cup.”
The game was played in front of 4,000 supporters as part of a pilot scheme, with research being carried out on allowing fans back in to sporting events as coronavirus restrictions are eased.
Tickets were limited to residents of Brent – the north London borough where Wembley Stadium is situated – and key workers.
Those inside Wembley witnessed a mainly dour game but Leicester, playing in their first semi-final since 1982, will not care – and neither will their followers.
Southampton were strangely lacking in intensity, barely threatening Leicester keeper Kasper Schmeichel. Ibrahima Diallo went closest to an equaliser for the Saints but his powerful drive went just wide.
Rodgers’ side will now face Chelsea in the final on 15 May, their first appearance in the showpiece since they lost 1-0 against Manchester City 52 years ago.