Shaw hasn't played since February 18 and won't be fit for the opener against Serbia.
"I felt something against Aston Villa and came off at half-time," Shaw said of a match played on February 11, a week before the Luton game. "It’s kind of everyone’s fault. Partly my fault, partly medical staff, I think everyone would admit that.
"The scan came back and there wasn’t too much there. But I didn’t train all week, then trained the day before the game. If the manager asks me to play, I’m never going to say no.
"I shouldn’t have played."
Shaw also said: "We all want to play football. My season has been so frustrating, injury after injury. Maybe at times, especially my first hamstring, could have been avoidable. That wasn’t the case, things happen, and I’ve just got to move on from that.
"The biggest thing for me now is putting my full focus on getting back fit and helping England win the Euros."
He added: "I would love to make the first game, I can’t lie. But I don’t want to rush too quickly because, realistically, I’ve only got one chance. If I feel something, then that’s it, and I don’t want that to happen."