Shearer is baffled by the praise The Three Lions received for their battling displays at the tournament in Poland and Ukraine under Roy Hodgson.
He told The Sun Sunday: "If we accept this level of performance, then we have given up on England.
"Have we dropped so far down the pecking order that we are applauding England for trying hard and being well-organised?"
He continued: "I cannot remember the last time the nation celebrated the team getting out of our group.
"That used to be the least that was expected. Now it seems to be a pointer that we are heading in the right direction. Well, we are not. We are getting progressively worse if you look at our performances in the last three major tournaments we qualified for."