"There was one player in an Everton shirt today who was, from the first second to the last, comfortable on the pitch", said the Dutch manager.
With the stage set, making his debut for the club at Goodison Park on the opening day of the Premier League season, fans now just had to wait for him to bag his first goal back at the club, and they didn't have to wait long!
Koeman also went for a three-man central defence that Stoke sought to disturb with a series of fine passes behind Everton's wing-backs, Leighton Baines and Dominic Calvert-Lewin, but they rarely threatened Pickford's goal during a tedious first half.
Despite the victory, Koeman admitted his new-look side was affected by nerves against a determined Stoke.
Rooney, who was full of invention and energy throughout, rose well to meet a fine Dominic Calvert-Lewin cross with a looping header into the far corner on the stroke of half-time.
The returning boyhood Blue popped up in first-half stoppage time to steer a header past Jack Butland with what proved to be the victor, although it took a terrific save from Jordan Pickford to preserve the points at the death in the second half.
Calvert-Lewin almost doubled Everton's lead when he robbed Zouma and cut into the penalty area for a drive that Butland pushed away.
"I expected to get space on that side [the right]". The changes brought immediate improvement from Everton who, with greater awareness from the England under-20 World Cup-winning striker, could have established a more comfortable lead.