Kylian Mbappe and Arda Guler struck for the visitors, with Huijsen shown a red card halfway through the first-half. Mikel Oyarzabal, from the penalty spot, struck for La Real after the break, but Real Madrid held on to win 2-1.
Huijsen was sent off for dragging down Oyarzabal as the last Real defender, but Xabi said afterwards: "For me it was a yellow card.
"Mili (Militao) was close and the ball wasn't under control. Watching the replay, I don't change my mind. I asked, he gave me his explanation, and I wasn't convinced. And I'll leave it at that. The context of the game changed, and we played with 10 men for 60 minutes.
"We had chances and scored the second, to give ourselves a margin. The team knew how to sacrifice, they were generous in their effort. Winning at Anoeta is always very difficult, and today, if possible, was even more difficult."
Xabi also said, "Four wins, but there's still a lot left. We have to keep building. The results are good, but the assessments in a context where we played with one less player are complicated."
On returning to his former club and also the pre-match tribute to John Toshack, he added: "I've watched all of Real's matches, and they should have more points. I'm sure the team will go up.
"There are some great players, and Sergio (Francisco) is also at a great level. He has a great hand to take us up the ladder. And the tribute is emotional because of what Toshack means. It's close to home for me, because he was the one who first gave me the confidence to be a footballer."