Rooney kept his composure to slot home a penalty in the final minute of normal time to salvage a point for the Merseysiders at Brighton.
At that point Everton were trailing to Anthony Knockaert’s 82nd-minute strike, and Koeman was facing a defeat that would have raised more questions about his side’s dismal start to the season.
But Rooney levelled and Koeman said: “Taking penalties is not the most difficult job but at this moment yes, because it’s totally different.
“It’s 1-0 down in a difficult situation and the team need points. If you keep your calmness in these types of situations that is experience and world class.”
Koeman was less forgiving about the defensive errors that allowed Brighton to take the lead.
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Dominic Calvert-Lewin was caught out as Brighton cranked up the pressure and the manager singled out Morgan Schneiderlin for criticism.
Koeman said: “Brighton were dangerous. They scored from one poor defensive moment. How we tried to block and not block the ball in two situations, first by Dominic – stay on your feet, don’t go down – and the same for Morgan in the second situation.”