Ancelotti won his first trophy in charge of Real, as the Spanish capital club claimed a 2-1 triumph over Barca in the cup final at the Mestalla.
Gareth Bale scored the decisive goal in the 85th minute, with the Welsh superstar vindicating Real's world-record transfer fee for the winger's services.
The 2007-08 term was the last when Barca ended a season without a trophy, which resulted in the sacking of coach Frank Rijkaard, and the Catalan club are facing a similar fate in 2013-14.
The La Liga crown is the only remaining title within Barca's grasp, and they are third in the race for it - four points behind leaders Atletico Madrid.
But despite Barca's struggles of late, Ancelotti said their Copa del Rey success did not mark the end of their El Clasico rivals' dominance.
"I don't think this means the end of the cycle for them. If we look at the game itself, they've done very well and have had their chances ... most of all when they equalised," the Italian said.
"They're a very dangerous team and although everyone is saying it's the end of a cycle, I don't see it that way."
Ancelotti's side, conversely, remain eligible to win the treble this season, and he said a final win would boost his squad's confidence - especially seeing they did it without star attacker Cristiano Ronaldo.
"They've all worked hard. We didn't have Cristiano, but the motivation of everyone else was at its peak and they worked even harder.
"This game gives us strength for the other two competitions."
Bale has scored 20 goals in all competitions this campaign, and Ancelotti hailed his recent addition - an extraordinary counter-attack goal that had the Welshman well off the pitch at one point - as the finest of his career.
"This is probably the most important goal of his career, because it's a defining moment," he said.
"He had a very good game, just like the rest.
"Real Madrid have played as a team. Only by doing that, can you beat Barca."
