Real defender Eder Militao was forced off after being poked in the eye and his replacement Nacho Fernandez also hit the woodwork.
"But for us even if we did lose it was all worthwhile because we had a chance to win a trophy that the club had never won before."
Fugazzotto almost always paints monkeys, in a variety of artistic styles, usually wearing human clothes and representing different cultures and historical periods.
Brighton remained in 13th, five points above the relegation zone, and manager Graham Potter was pleased by the south coast side's latest display.
"They are the champions, they have all the assets to be called the best team in Europe. We will have to use all our hard work and our experience.
European champions Liverpool travel to Madrid in February for the Champions League first leg match and will have noted the commitment inspired by Atletico's feisty Argentine coach Diego Simeone.
He left the club in 2008 to return to Chinese football, and retired aged 30.
"Security people were like fathers to us. They kept talking to us and they were right behind us every time. When we were going out to eat or shopping, they were there."
Jurgen Klopp's side will travel to the Wanda Metropolitano, where Liverpool lifted the trophy in June, for the first leg of their tie against three-time runners-up Atletico.