Gordon Strachan admitted his players let themselves down and were "spooked" by England's aggression and intensity in Scotland's 3-1 friendly defeat at Parkhead.

Wayne Rooney's two goals, after Alex Oxlade-Chamberlain's opener, killed the atmosphere for the bulk of the 49,526 crowd.

Andrew Robertson's late goal was ultimately meaningless as Scotland were well-beaten by Roy Hodgson's side. The first Auld Enemy clash in Glasgow for 15 years ended up became an anti-climactic end to Scotland's otherwise encouraging year.

Manager Strachan was predictably downbeat but talked up the greater significance of beating the Republic of Ireland in last Friday's Euro 2016 qualifier.

"When we met ten days ago, the point of the exercise was to get three points against Ireland, which we did. I thought the intensity, pace and strength England played at was fantastic; without the ball, especially. It kind of spooked our players.

"I think England must have watched our game against Ireland and thought 'right, we'll go for them'. They did that, when our players were maybe expecting them to sit back and wait. England have a team full of Champions League players and they showed that tonight. We were maybe mentally fatigued from Friday, which is something we need to look at."

The lead from Oxlade-Chamberlain's first half goal was doubled soon after the interval when Rooney capitalised on careless defending. Robertson pulled one back near the end only for Rooney to quickly capitalise on further Scottish carelessness.

"When it was 1-0, I thought 'okay, there's not been many attempts in the game'," said Strachan. "I felt if we played better we could get something out of the game. But then two minutes into the second half we gave the ball away and lost the second goal.

"That was a feature of our play, giving the ball away under pressure and also without pressure. The team who looked after the ball better was England. Unless you are very, very lucky, the outcome is going to be what you got tonight.

"I'll try and keep Irish game fresh in memory, and it will be in a few weeks. At the moment, we have to deal with this game and it's not great fun. We let ourselves down, to be honest. We haven't let ourselves down over the past ten days, but we have in this game.

"We are disappointed with the performance. We know we can play better but we need to be at our maximum to play against a top side like that. That's probably the best performance against us for a long time.

"Some of our players came from Championship football and they were playing against Champions League players. It is a big step up. When you take on a good England side, which they were tonight, you need 10 out of 11 of your players at their best to beat them. We didn't have that tonight. As a group, we are disappointed, that's for sure.

"Would I reconsider not making more changes from Friday in hindsight? It could have been 2-0 or 3-0 at half-time if we'd done that. It's something I have to think about. Do we have a huge squad we can chop and change if we want to beat the top teams? I don't know. That was a one-off game tonight."

Scotland's next scheduled game is at home to Gibraltar when the Euro 2016 campaign resumes on March 29.

Hodgson was delighted with England's performance and said he had enjoyed his two games against Scotland - England won 3-2 at Wembley 15 months ago - but meeting regularly was problematic.

"I thought we showed our intentions from the off and started the game very well. I can't think of many periods in the game where I was concerned we were losing control. We managed to quieten them and give our own fans something to cheer about.

"The problem [with meeting more often] is the few opportunities you get in the FIFA calendar. I've enjoyed the two matches I've had. I've played in front of a full house at Wembley and now at Celtic Park, two really important fixtures for Scotland and us. I'm delighted to have those games on my cv.

"If it should be put in a future calendar, I wouldn't say no. But it's not as simple as all that."