The 41-year-old trainer believes his team deserve their place in the semi-final of the cup, and was also keen to play down the Blancos' second-half comeback at Camp Nou
Despite Madrid making an impressive start to the game, it was the Blaugrana who were cruising at half-time with a 2-0 lead courtesy of strikes from Pedro and Dani Alves.
However, second-half strikes from Cristiano Ronaldo and Karim Benzema made for a tense finale, with Jose Mourinho's men pushing for the goal that would have taken them through.
Yet Guardiola was reluctant to heap heavy praise on his opposition, who were reduced to 10 men late in the game.
"Madrid only did what we would have done in their situation. The [Barcelona] players showed great strength and I congratulate them. Madrid are a great team and therefore this merits our victory, Madrid played a good game, but we were the victors over the 180 minutes," he told reporters after the game.
The 41-year-old also played down claims that it was his most stressful game in charge of Barcelona, with the coach looking back to a Primera Division encounter versus Sevilla in 2010.
"I suffered more in Seville [in 2010]. We were winning 3-0 but then they pulled it back to 3-2 and if we had conceded again, we could have lost the league," he added.
The former Barcelona B man concluded his post-match comments with a few words on his opposite number, Mourinho, who he refused to criticise.
"With respect to my colleague [Mourinho], I want to thank him for congratulating our party at the Bernabeu," he stated.
Barcelona return to Liga action this weekend when they face a trip to out-of-form Villarreal.
Starting in November and continuing through to the middle of February, Goal.com is publishing exclusive extracts from Graham Hunter's highly-anticipated new book, 'Barca: The Making of the Greatest Team in the World'. Friday's extract looks at how Barca suffered rare disappointment at the hands of Real Madrid in a gripping finale to last season's Copa del Rey. Don't miss it!