England set the pace early in the match, Raheem Sterling hitting the post in the second minute when he lifted the ball past advancing keeper Tomas Vaclik and finding the back of the net 10 minutes later with a close-range header.
Czech coach Jaroslav Silhavy said his squad settled well after that but were still the poorer side in attack.
“The finishing wasn’t really great today and England was stronger in that aspect,” he told reporters.
Tomas Soucek, who fired wide from one of the Czechs’ best chances, said the team needed to control the ball better.
“We need to improve the control of the ball around the opposition’s box. We had good chances, but we did not complete the (attack) phase,” he said.
The tall midfielder said the second half was more even and the Czechs managed seven attempts on goal with one on target when Tomas Holes was denied.
The Czechs have been over-reliant on striker Patrik Schick, who scored three goals in the group phase, and know they must come up with more attacking options.
After finishing third in Group D, they move on to face either the Netherlands, Belgium or the Group E winners – Sweden, Slovakia, Spain or Poland.
Coach Silhavy said a game in Budapest, which is 525 kilometres from Prague and where the Dutch are slated to play, would be a big draw for Czech supporters.
“I would probably wish for Budapest just because of the fans,” he said.