The capital club triumphed 4-1 at Almeria but after a scratchy first half, Real looked set to be reeled in at 2-2 just after the hour mark, when Marcelo fouled Edgar Mendez in the box.
Almeria's Verza, who had struck the home side's earlier equaliser, stepped up to the spot but his tame effort could not beat Casillas, who dived smartly to his left to palm the shot away.
"It was a key moment," Casillas said after the game.
"If we had let the goal in it would have been different because they would have equalised but the team reacted and really got into the game. We leave here happy."
Ancelotti added: "The penalty save was a decisive moment and everything got easier after that."
Having remained in front, Real wrapped up their three-goal victory in the final 10 minutes with Cristiano Ronaldo striking twice in seven minutes to stretch the winning streak of Ancelotti's side to 20 matches in all competitions.
"It wasn't smooth sailing," Real's coach said.
"They put a lot of pressure on us but our quality came through and we were able to win."
Real had led 2-1 at half-time through a fine goal from Isco and a header from Gareth Bale, split by Verza's blistering strike from 20 yards.
Casillas conceded the visitors had not been happy at the break, despite their advantage.
"During the break we mentioned that this wasn't our best game, we were lacking intensity," the goalkeeper said.
"At the end of the day, we finished the game resoundingly, although it was a hard-fought battle to get to 4-1."
The victory capped off Real's year in La Liga with the capital outfit moving five points clear at the top of the table ahead of the Christmas break, although Barcelona (34 points) and Atletico Madrid (32) will be expected to reduce that margin when they play on Saturday and Sunday respectively.
Real will now turn their attention to the Club World Cup, where they will face either Cruz Azul of Mexico or Australia's Western Sydney Wanderers on Tuesday.
Ancelotti was not interested in playing down expectations ahead of his team's trip to Morocco, with six of the past seven editions having been won by European teams.
"We finished the year well in the league and now it is time to concentrate on the Club World Cup, we have to win it," the Italian said.
"If I had to give the team a grade, they would get a very high mark. We aim to win every competition we play in. There is a good atmosphere and we will go out there to win."
