Meanwhile, Tottenham striker Harry Kane will continue to lead England against France, having captained the national side on Saturday - a game which saw the 23-year-old score a late equaliser at Hampden Park.
England took the lead in the 70th minute when substitute Alex Oxlade-Chamberlain's left-foot strike beat goalkeeper Craig Gordon's flimsy attempt at a save.
Harry Kane's injury-time equaliser rescued a point for England.
Kane, who was handed the captain's armband for the first time, said: "I would say that is probably the most special moment for me". To go 2-1 behind out of the blue like that with two special free-kicks from Griffiths, it was unbelievable character to come back a get a point.
"I'm disappointed that someone of Joe's size never got across. I was trying to get a good contact on it and side-footed into the net", he told ITV. "We have four games left and we could win all of them".
"We have to be a team that are never beaten".
Kane's goal was his sixth in 18 worldwide appearances and came at the end of his first game under Southgate, after injuries had kept him out of England's six previous matches.
The Celtic man added: "I am delighted to get off the mark for Scotland, in what could have been a great win, but in the end this could be a great point for us". They were like a heavyweight boxer and we were middleweight, which we expected.
But last season he was dropped by club manager Pep Guardiola, who sent him out on loan to Italian side Torino and last week signed his replacement at Man City: Brazilian keeper Ederson has joined for what British media reported was 35 million pounds ($44.59 million), a world record fee for a goalkeeper.
"You have to somehow find another gear and now it is not a bad point away from home".
Scotland had started the game aggressively, roared on by a capacity 52,000 crowd but England gradually took control and ended the first half looking increasingly unsafe.
"The first one has come through a lot of bodies", he said. "It got us back into contention and if we can perform like we did in that match, then we will certainly cause England a few problems".
"I think we had three down with cramp as well".
"We could have had maybe a four versus two going up the field and we could have just killed the game off", said the Hull City defender.
"We look at opposition set plays before every game and we knew Griffiths had a great free-kick on him", added Kane. "Butland was in pole position before he got that injury in Germany a year ago".
"We have really good cover in most positions but defensive midfield is an area where we're a little short".