La Blaugrana were two goals ahead and 4-1 up on aggregate at half time following goals from Pedro and Dani Alves, but a second-half fightback – in which Cristiano Ronaldo and Karim Benzema grabbed a goal each – saw Los Blancos fall one score short of a win.
However, the Barca boss insists that his side deserve to be in the semi-finals.
"The players showed great strength and I congratulate them," he told reporters. "Madrid are a great team and therefore this merits our victory.
"We were the victors over the 180 minutes. Madrid only did what we would have done in their situation."
Meanwhile, Jose Mourinho's side maintain their five-point lead over Guardiola's men in La Liga.