Watch: England fans sing Three Lions at Wembley
The comedian, 57, recorded the track with Frank Skinner and the Lightning Seeds for the Euro 1996 tournament, where England were knocked out in the semi-finals by Germany.
On Tuesday night, Three Lions was sung by fans at Wembley as Gareth Southgate’s team secured victory over their old rivals with second-half goals from Raheem Sterling and Harry Kane.
Baddiel, who was in the crowd with Skinner, told Today on BBC Radio 4: “It feels like it is a huge narrative arc for me and Frank Skinner and for our song because of course we were there in 1996 when Germany destroyed the dream of that particular summer.
“And we have actually been together at other England and Germany games that England have crashed out of major tournaments at.
“So it just felt unbelievable to think that we might win this one. At the start of the game I was tense for quite a long time, until Jack Grealish came on and changed the game.”
Baddiel said Sterling’s second-half goal had left him “blind with joy”.
He said: “It is one of those moments where – I was there with my son as well as Frank and Frank’s son – and then everyone around us are just blind with joy for a little while.
“You just can’t think about anything apart from the euphoria you are feeling in that moment.”
Baddiel said the win may offer former player Southgate redemption, after he missed a pivotal penalty against Germany during the Euro 96 match.
He said: “Probably somewhere deep in Gareth Southgate’s subconscious it does.
“He did do an interview the other day where he said: ‘I’m not interested in talking about the past and some of the players weren’t even born when that match happened.’
“And it didn’t go to penalties. It being the German side, I think it would have been almost impossible for certainly everyone in the crowd who remembers it not to think: ‘Oh no, is it going to be that thing? Is it going to be the Southgate moment?’”
Writing in the Evening Standard, Baddiel explained how he and Skinner had wanted to write a song about the passion of fans and England’s tendency to lose important games.
He said: “Three Lions is a song about loss: about the fact that England mainly lose. We as fans — as English people — invest an enormous amount in the idea of England, and then, as experience suggests, England let you down.
“We know this and yet we still — as the 98 version put it — believe. Football fandom is this, it’s magical thinking, it’s hope over experience.”