Fourteen-times champions Madrid held on to dispatch the holders 4-3 in a shootout at Etihad Stadium to secure their semi-final berth against Bayern Munich, sweet revenge after City ousted the Spaniards in last year's semis on their way to winning their first title.
"Congratulations to Real Madrid, they defend so deep, with incredible solidarity," Guardiola said.
"We did everything. I have no regrets about what we've done. Defensively, offensively, we played exceptional in all departments, in everything, and unfortunately we couldn't win, so that's what it is."
After capturing their first treble - Champions League, FA Cup and Premier League titles - last season, they appeared on track to become the first team in history to claim the three titles in back-to-back years.
But despite completely dominating Madrid, firing 33 shots to Madrid's eight and taking 18 corners to just one for the visitors, Guardiola's men could not finish them off.
Kevin De Bruyne scored in the 76th minute to cancel out Rodrygo's 12th-minute goal, but both the Belgian and City's goal-scoring machine Erling Haaland squandered several scoring chances as the tie finished 1-1 on the night and 4-4 on aggregate.
Victory looked in City's hands when Luka Modric failed to convert Madrid's opening spot kick, but momentum swung when Bernardo Silva shot straight into keeper Andriy Lunin's hands, leaving Madrid's Nacho and Antonio Rudiger to seal the win.
"Pep Guardiola is a gentleman, always has been," Madrid manager Carlo Ancelotti told Movistar. "He congratulated us, wished us good luck and that's what a real gent does."
Despite the heartbreaking ending, City fans serenaded the team off the Etihad pitch.
"Football is about scoring goals and from the penalty spot they did it a bit better than us," Guardiola said.
"The performance and the commitment and everything was exceptional. With penalties, you win some, you lose some. For the way we played, we should have done it before. But we did not convert the chances we had. We performed to our best, but it was not good enough."
City now switch their focus to their quest for another FA Cup title on Saturday when they clash with Chelsea in the semi-finals at Wembley.
Asked how he will pick up his players, Guardiola said: "We'll see tomorrow. Now it's rest. It's the semi-final of the FA Cup, we will try to compete the best we can."
Guardiola's team also have a two-point lead at the top of the Premier League with six games remaining.
