Southgate twice convinced Walker not to retire from England duty
Walker scored his first-ever England goal in his 77th appearance during Saturday's 1-1 draw against Ukraine in Wroclaw.
The Manchester City right-back's memorable moment in the Euro 2024 qualifier came after his future for both club and country was uncertain during the close-season.
Only an intervention from City boss Pep Guardiola saw Walker stay with the treble winners after Bayern Munich expressed interest in the 33-year-old.
Southgate revealed he also had to change Walker's mind after both the Euro 2020 final defeat to Italy and last year's World Cup in Qatar.
"I've talked him out of retirement twice from international football," Southgate said.
"After the Euros and after the World Cup, I think he loves being here and he's wanted to keep going and now he's thinking about how many caps can he get.
"He's critical to us. If we're talking about world-class players in their position in our team then he's probably one of them.
"I think he didn't realise how much value we have for him and how important he is for us. He's probably not going to thank me for sharing that!"
Southgate has given Walker all but 20 of his senior England caps and he praised the defender for continuing to improve in the latter stages of his career.
Asked if Walker has got better with age, Southgate said: "I think he has.
"It doesn't always happen but he's not only playing but also seeing him around in training, the way I hear him speak when he's interviewed, his influence on the group, he's become a really mature leader for us.
"Two or three days into the training his focus was really clear, the way he was organising on the pitch and I think he's enjoying the extra responsibility he's had at his club and I know he's ready to embrace that with us as well."
England face old rivals Scotland in a friendly in Glasgow on Tuesday, a fixture Southgate believes will be a valuable test as his side prepare for Euro 2024.
Southgate's group leaders are within touching distance of securing their place in Germany, with Scotland also on course to qualify after beating Cyprus on Friday.
"Another hostile environment, a team that are playing really well," Southgate said.
"You know, they're in great form, full of confidence so it's another important learning step for us."