The Three Lions warmed up for the tournament with a 3-0 win over Peru on Friday, but a lack of fluidity in midfield often stifled their play.
Writing in his column for the Daily Mail, Keown said: "On Friday night in the first half there was too big a gap between Steven Gerrard, Jordan Henderson and the front four. If you have two midfielders sitting then you need five or 10-yard passing options in front of them to move the ball quickly.
"Gerrard sat deep but Henderson did not bomb forward as often as he does for his club. There were moments of quality — Daniel Sturridge's goal was outstanding — and things improved in the second half but there were too many straight, long passes.
"England looked much better when there were more short options."
England will now travel to Miami to play two friendlies against Ecuador and Honduras next week.