England lost 2-1 in the final minutes to the Czech Republic to be eliminated.
Owen tweeted: "Initial reaction is to say that sums England up at major tournaments but I hate being negative or defeatist. Or is that just the reality?
"Lots of you saying we don't keep the ball well enough. Probably an English trait as the way we set up our teams makes it difficult to do.
"Look at Barcelona. Their striker is Messi. Nobody can tell me he stays up front. Keeping the ball is easier when you flood the midfield."