England won 2-0 thanks to an own goal and Arsenal midfielder Declan Rice's effort on Saturday.
Former Republic of Ireland captain Keane said afterwards: "I don't think the manager (Thomas Tuchel) is too happy at the end.
"I think he'd be frustrated again with the second half. We're on about setting high standards and getting into good habits.
"I still think England fell back into their old ways again tonight. Certainly in the second half. Sidewards, backwards passes.
"We saw their two goals tonight, particularly the second one. Just from a cross. They've got to cross it a bit more. Don't complicate the game. And I still think they've gone backwards too many times."
He continued: "Especially if you've got players like Reece James in possession. We saw the goal, it was very straightforward.
"Obviously he gets a good first touch and Declan just walks in there and the beauty with the cross, it's almost set up for it because they've been used to dealing with balls in front of them.
"I watch all levels of football, as we all do. The amount of goals that come from crosses.
"England's two goals today come from crosses. Don't be reluctant to cross the ball."