England won 3-0 at Wembley on Friday to boost Southgate's chances of being given the job full-time
England's interim manager Gareth Southgate and his Scotland counterpart Gordon Strachan refused to be drawn on their respective futures following the World Cup qualifier between their teams.
England won 3-0 at Wembley on Friday to boost Southgate's chances of being given the job full-time, having won two and drawn one of the first three games in his four-match tenure.
But Strachan may have overseen his last game as Scotland manager, the result leaving his team six points adrift of Group F leaders England with only minnows Malta below them.
"At this moment in time, if you think I'm thinking about myself, then you don't know me," Strachan told reporters when he was asked about his position.
"You absolutely don't know me. If you think I'm sitting here, worrying about myself and how I'm feeling, you're wrong. Completely wrong.
"You think I'm thinking about myself when all these guys have gone through that, all their families have travelled down here, the supporters travelled down here?
"When will I think about myself? Probably when I'm just about to die. I'll say: 'How did you get on, Gordon?' 'Not a bad life'. Apart from that, no.
"It's absolutely nothing to do with me. I have to think about everybody in that dressing room and how I send them back to their clubs not (feeling) down.
"I've got to send them back feeling they gave it their best shot."
England prevailed courtesy of a trio of headers from Daniel Sturridge, Adam Lallana and Gary Cahill, which kept them two points clear of Slovenia at the group summit.
But Scotland started the second half strongly, going close through Jamie Forrest, before Lallana doubled England's lead and Strachan felt the scoreline was not a fair reflection of the game.
"The game was cruel to them tonight, really cruel," said the former Celtic manager, who took over from Craig Levein in January 2013.
"In life, if you put that much work in, somewhere along the line the game has got to get good for you."
Southgate was hastily promoted from his role as England Under-21s coach in late September after Sam Allardyce fell foul of a newspaper sting.
He began his tenure with a laboured 2-0 win over Malta, followed by an unimpressive 0-0 draw in Slovenia, but his side presented a much sharper cutting edge against Scotland.
With England set to tackle Spain in a friendly at Wembley on Tuesday, Southgate said he would not waste any time fretting about the likelihood of him landing the role full-time.
"That's not my decision. I was given the task of picking the job up in a very difficult situation for everybody and I feel we've prepared the team really well," he said.
"I've enjoyed working with them. We have a difficult challenge against Spain, a great test for us, and the rest is out of my hands."
Asked if the experience to date had whetted his appetite, he conceded: "I've loved it. I've really enjoyed the role and the responsibility, the challenge of every part of it.
"I get that that's not quite as enjoyable if you don't get the results. There are nights where you have to get over the line and get the result, but it's been a brilliant experience."