Wayne Rooney was the match winner on his return to his boyhood club with a well-timed header as the match ended 1-0.
While Koeman hailed the result, he admitted his side ‘didn’t play well’.
He told Sky Sports: “I’m happy with the points. Maybe every manager before the start of the season thinks that their team is ready and prepared but it was really a difficult game.
“Stoke made it really difficult and if you know that, and you keep the clean sheet and the points at home, it is a perfect result. It was a win and that’s what you like to have after the first match.”