The defender started the friendly at the Wörthersee Stadion and played 75 minutes before being substituted.
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Speaking to Realmadrid TV afterwards, Dumfries reflected positively on his first appearance for the Spanish giants.
“I felt good, and I am very proud to debut with Real Madrid. It was a great experience, this first match, and now it's time to work hard for more games,” he said.
“It’s the first match, and I’ve just returned to training, but Mourinho asks me to work hard and show my worth.
“It wasn’t my natural position, but it was a good friendly match. I can play in different positions, and I’m used to it, though I usually play on the right.”