Real Madrid 'absolutely' have confidence in Rafael Benitez
Benitez's men finished the year in fine style, recording a 3-1 win over Real Sociedad on Wednesday.
The Spaniard has been under increasing pressure due to his team's performances, but Madrid sit just two points behind La Liga leaders Barcelona – who have a game in hand.
Asked if he had confidence in Benitez, Butragueno told Movistar+: "Yes, absolutely."
Madrid will finish the year without a trophy, having claimed four during 2014.
Butragueno hopes a new year will bring different luck for the La Liga giants, who kick-off 2016 with a trip to Valencia on Sunday.
"Last year we had gotten to this point with four titles. We came to win the Club World Cup," he said.
"[This year] has been different...I hope 2016 is good, because we do well in even years."