Speaking ahead of Friday’s Euro 2020 clash with Scotland, the England manager recalled their 3-0 win over the same opponents in November 2016 in his third game in temporary charge.
Southgate was initially reluctant to take the job on a permanent basis but revealed he would have regretted not taking the risk, and said Eriksen’s scare last Saturday was a timely reminder.
The Denmark midfielder’s heart briefly stopped during their opening match of the tournament against Finland and he is recovering in hospital after being resuscitated on the pitch.
Asked if the comfortable win over Scotland in 2016 had persuaded him to take the England job, Southgate said: “What persuaded me was that the players were willing to adapt to the approach that we had and embrace the way we wanted to play and the way we wanted to work. The win just allowed that to happen.
“The win did not convince me – perhaps it persuaded everybody else to think, ‘Blimey, we’ve tried everything else, perhaps we might give this bloke a go – he took the under-21s, let’s go from there!’
“On a personal level, by the time we got there I felt it was a job I wanted even though I was never going to say that publicly. But I knew having worked with the players and having had a closer insight into the workings of the job, it was something I wanted to go for in my life.
“I had kind of regretted not having had a go at it and would never have known what might have been possible. That is not a good position to be in, in your life.
“When we saw what happened with Christian Eriksen the other day, it was just another reminder that you have got to go for things in life and give them the best possible shot.
“At least when you’re finished, you don’t have regrets about things you did not have a go at or performances that were inhibited. We have got to go for it.”
Southgate succeeded Sam Allardyce with the national team at a low ebb, having been knocked out of Euro 2016 by Iceland before Roy Hodgson’s successor was dismissed after one match following a newspaper sting.
The then-England U21 coach led the Three Lions to an unconvincing 2-0 win over Malta - in which captain Wayne Rooney was booed by his own fans - and a dull 0-0 draw with Slovenia before thrashing the Scots.
Southgate admitted he would not be England manager were if not for the win at Wembley, but said he would be judged on performances at major tournaments.
"If we had not beaten Scotland, you would not be speaking to me here," he said.
"Also, that moment for Scotland was a difficult one – they were in the middle of a bad run of form and that fell quite kindly for us as a fixture.
"I felt we played well on the night, but we were in the really early stages of getting the team to resemble what we truly believed and what the consequences of more time coaching the team allowed to happen.
"Tournaments define England managers, there is no doubt about that. If you look at our history, most of our win records are reasonably similar but the tournament performances define you.
“We are aware of that and know they are the things that really matter for the country and really matter for the team."
There was little in England's performance against the Scots five years ago to suggest Southgate was on the verge of ushering in a bright new future, but the manager has since led them to a World Cup semi-final and they can reach the Euro 2020 knockouts with a game to spare with a win over Steve Clarke side's.
Southgate also revealed the reverse fixture against Scotland at Hampden Park in June 2017 had been a pivotal moment in his tenure, helping to persuade him to put more faith in the next generation of "fearless" talent.
Leigh Griffiths twice scored direct free-kicks, the second in the first minute of stoppage-time, to give Scotland a 2-1 lead - but Harry Kane equalised with the last kick of the game.
"We learned a lot," Southgate said. "I think for this team it was moment where they didn't panic when they went behind and that was very important.
“We felt like that had happened in the past. They showed themselves that they could come back from difficult situations in games and we've been able to so do that in the past few years.
“That's a strength. I think good teams win games late. They are capable of coming back from setbacks.
"It also taught me that sometimes you can go with experienced players and expect them to handle those sorts of – and actually it doesn't always work out that way.
“You know, it was probably one of the moments when I started to think about younger players coming in, who were a little bit more fearless perhaps. Going a slightly different route.
“So in many ways it was afternoon, the atmosphere was as good as I've been involved in, there's no doubt about that, it was definitely, aside from that, an afternoon that taught us a lot."