Real rounded off 2014 with a 4-2 friendly defeat to Milan, but that result did nothing to take the shine off the club's astonishing form at the back end of the calendar year.
Victory over San Lorenzo in the final of the Club World Cup provided European champions Real with more silverware and extended their winning streak in competitive action to 22 matches.
Ancelotti is confident more success can be achieved in 2015, highlighting the strength in depth at his disposal.
"In 2015 we want to compete in every competition. We have a very strong squad and we have the confidence to compete for everything," Ancelotti told Real's official website.
"It is clear that winning the Champions League in 2015 would be a dream and we will try to do it. Real Madrid are always the same, we try to win everything possible.
"We are confident because the squad is very strong, the strongest in the world. We have to work and fight in order to try and win again."
Ancelotti's words were echoed by experienced goalkeeper Iker Casillas, who added: "I think that area by area we have the best player. We can compete for everything given that we are such a competitive team."
Real begin the new year with a trip to Valencia on Sunday.
