Wayne Rooney scored twice while Alex Oxlade-Chamberlain also netted as England came away from Glasgow with an excellent friendly victory.
And Strachan, who said Scotland's passing was not up to scratch, acknowledged England's performance with praise.
"We're disappointed, at the end of the year, to finish it with defeat," Strachan told Sky Sports.
"There could be a couple of things that made that happen.
"One was definitely an England side that were determined and as intense as I have seen them for a long time.
"I think that goes down a lot to what they might have thought happened if they didn't do that.
"I think we've got to say well done to England. That's a team full of Champions League players.
"I think England spooked us with their intensity early in the game.
"We could have passed the ball better, that's for sure. But I've got to say that England were after us and they tested that."
Strachan, who felt his side were "mentally tired", still reflected positively on Scotland's week.
Scotland beat the Republic of Ireland 1-0 in a Euro 2016 qualifier on Friday - a result that moved them level on points with second-placed Germany in a hotly contested Group D.
"We got together…10-12 days ago - our objective was to get three points against a good Republic side," he added.
"We've got that. We're pleased with that."
