The Qatar-backed Ligue 1 club overcame the early dismissal of star striker Zlatan Ibrahimovic at Stamford Bridge on Wednesday night to knock Chelsea out on away goals after extra time.
"I am not surprised that PSG, even with one man down, beat Chelsea," Platini said in Lyon on the sidelines of a committee meeting for Euro 2016, to be hosted by France.
"It's a great achievement. They are already ready to win the tournament, they have the team to win it. They are programmed to do so," the Frenchman added.
Held 1-1 in their last 16, first leg, tie at the Parc des Princes, the Parisians advanced by twice coming from behind in the second leg.
Captain Thiago Silva scored an extra-time header for 10-man PSG to clinch a 2-2 draw, leaving it all square at 3-3 over the two legs and sending the Parisians through on away goals.
The French press hailed the achievement on Thursday which sports daily L'Equipe headlined as 'Heroic'.
"A Capital Exploit," the newspaper continued, saying the victory "was among the most glorious nights in the Parisian club's history", on a par with victories over Real Madrid in 1993 and Barcelona in 1995 when they reached the semi-finals of Europe's elite competition.
"The Parisians qualified for the Champions League quarter-finals by being stronger than Chelsea and fewer on the pitch," L'Equipe said. "Above all, don't stop," it urged.
PSG president Nasser Al-Khelaifi agreed that the PSG "project was on the right track".
"Qualifying here (in London), against (Jose) Mourinho's Chelsea was difficult. Before the game, I told the players face to face that we could do it. Everyone believed it. I'm very proud," said the Qatari businessman.
"We played over 95 minutes as warriors, in an incredible atmosphere which made us think we were at home.
"Since we bought the club (in 2011), we have believed in our European ambitions. After beating a team such as Chelsea, I believe we can go far. Our project is on the right track."