The Spaniard added, "Madrid played better than us".
But in the 15th minute of the match, Ronaldo nearly came to blows with PSG full-back and former El Clasico rival Dani Alves, after appearing to kick out at the Brazilian veteran.
Nevertheless, Real Madrid marched on to the quarter-finals in a performance which will have delighted Zinédine Zidane.
Cristiano Ronaldo's powerful header - his 12th goal of the competition - and a deflected effort from midfielder Casemiro either side of a close-range finish from PSG's Edinson Cavani sent Madrid through 5-2 on aggregate. "For the moment, we can not get past the last 16, but that will change at one time or another, I am sure of that".
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For PSG they will have to wait another season to get their hands on the Champions League trophy but for Real Madrid they have a chance to win their 3rd consecutive Champions League campaign. Yes they were unlucky to be drawn against Madrid after topping their group, and also to lose Neymar to injury, but once again they fell short when it mattered. We will continue with what we are all doing.
"Our fans got behind us, I apologise to them", Rabiot said.
When I came here I said I was sure this team can win the Champions League. We played a serious game from the beginning, played high, pressing.
"We will need a different level of intensity than in the first leg, but we are ready", said Zidane.
They took their spending spree to a whole new level a year ago, spending a world-record 222 million euros ($264 million) to sign Neymar from Barcelona and committing 180 million euros to sign Kylian Mbappe from Monaco. Back on home soil, he picked up a vital win, keeping his side's hopes of silverware at the end of a terrible season alive. After allowing three unanswered goals in a 3-1 defeat to Real Madrid at the Bernabeu, a comeback became even more unlikely when Neymar injured himself right before his sister's birthday.