Speaking on the club's website Al-Khelaifi, the figurehead of PSG's Qatari owners, was pleased with a performance to match the sums of money spent on bringing star players to the capital over the past 24 months.
Major summer signing Edinson Cavani opened the scoring only for Vladimir Weiss to equalise before the break.
PSG took charge in the second half, however, with Thiago Motta heading in quickfire goals before Marquinhos added another late on.
There was even enough time for Zlatan Ibrahimovic to miss a penalty as the French side showed they are ready to improve on the quarter-finals finish of last term.
"It's a very good result because it was a very difficult victory," Al-Khelaifi said.
"Paris Saint-Germain played very well in the second half. It's very good to score four goals away, in this stadium, in our first match in the Champions League.
"Like I said at the draw, there are no easy matches in this competition, but we are very ambitious."
Coach Laurent Blanc admitted his side had saved their best for the second half.
"It was a match of two halves," he said.
"We made too many mistakes in the first half, mostly because Olympiacos put a lot of intensity and pressure into their game in the early stages.
"In the second half, we found a certain balance and, as a team, we were a lot better. The Greek side also tired after a very energetic opening period."
Motta was pleased to make a difference as he first headed in half-time substitute Ezequiel Lavezzi's corner before the pair combined again moments later.
"We work a lot of set pieces in training and I was lucky enough to see it come off for me," he said.
"The three points are the most important thing and it's perfect to make a winning start to the competition."