Predictions of a comfortable win for the hosts proved unfounded as Steve Clarke's men matched, and at times bettered, their old rivals to deservedly collect their first point of the tournament against the odds.
The courageous display left Tartan Army dancing in the rain and means that victory over Croatia in their final Group D match on Tuesday could be enough to see Steve Clarke’s men into the last 16.
"I thought the boys ran the legs off themselves," said McGregor, who excelled in the holding midfield role alongside Chelsea’s Billy Gilmour "Tactically I thought we were excellent. There were real periods where we had to control the game without the ball and when we got it we played really well.
"We were comfortable in possession, we built our way up the pitch and we created chances as well. It was a great night for us and we've given ourselves a chance for Tuesday.
"The [England] team is full of good players and the challenge for us was to take the challenge on, accept it and I thought everybody to a man was absolutely outstanding.
"We have to stay calm, stay relaxed and we go again on Tuesday."
The Celtic midfielder was one of four changes from the side that opened the tournament with a disappointing 2-0 defeat to Czech Republic at Hampden on Monday, along with Gilmour earning his first international start, Che Adams restored up front and Kieran Tierney returning to the line-up after missing the first game through injury.
The response was emphatic as Scotland produced a far more impressive display, restricting England to limited opportunities while posing a threat in attack to put the Czech result behind them.
"There's always massive energy when you get there for the first time in 23 years and it's a bit like the bubble's burst and you have to go again," McGregor reflected.
"Credit to the players, I thought we reset ourselves really well to come into an arena like this and everybody showed personality and we took the ball.
"We were a real threat in the game and we defended when we had to. We've arrived now and we've got our first point. Now it's on to Tuesday.
"It's a great night, you see the support, it's so loud, and you can hardly hear yourself think on the pitch, but we've given ourselves a chance for Tuesday now so we have to recover.
"Great team spirit, great energy, we just have to harness that for Tuesday now and we go and try to get through the group."