In a mouthwatering play-off tie drawn at UEFA headquarters in Nyon, the two former European champions were pitted against each other for just one slot in the competition proper.
Although Milan have enjoyed more recent success on the continent than their opponents, Gandini is fearful of a rejuvenated PSV side.
"The PSV games will be the most important games of the season," he told the Corriere dello Sport. "Reaching the group stage is our top priority but it will not be easy to go through.
"Even though they have sold some key players, PSV are a very strong team. According to UEFA club coefficients they were the strongest opponent we could meet."
The Eindhoven club, who won the European Cup in 1988, look a different proposition under coach Philipp Cocu after selling star players Kevin Strootman, Dries Mertens, Erik Pieters and Jeremain Lens.
Young talents Stijn Schaars, Santiago Arias, Florian Jozefzoon, Adam Maher, Karim Rekik and Jeffrey Bruma have since arrived at the Philips Stadion, and the Dutch club's general secretary Ron Verkerk is looking forward to a bright future.
He said: "I'm not sure that Milan are the worst possible draw for us.
"We may have less experience than Milan and we have sold some key players, but we then took on some talented young people.
"We are confident that in the next year or two, our team will be very competitive. We could even spring a surprise in these Champions League games."
Arsenal will face Turkish club Fenerbahce, who are awaiting a final ruling from the Court of Arbitration for Sport (CAS) over whether they will be allowed to feature this season, having been banned from European competition by UEFA for alleged match-fixing in the Turkish Super Lig.
They have challenged that ruling and a CAS verdict is due before the group stage draw is made, but home and away matches against Arsenal stand to go ahead before that decision arrives.
UEFA today said no decision has yet been made regarding what would happen in the event of Fenerbahce winning the tie and losing their CAS appeal.
Celtic have been drawn against Shakhter Karagandy of Kazakhstan in what appears a favourable draw, travel notwithstanding, for Neil Lennon's team as they bid to reach the group stages.
Celtic came through 1-0 on aggregate against Elfsborg in the third qualifying round, winning at Parkhead and then holding on for a hard-earned goalless draw in Sweden on Wednesday night.
The Glasgow club face a team who have no European pedigree and who are aiming to reach a main-draw stage for the first time. Celtic, by contrast, won the European Cup in 1967.
Shakhter landed the Kazakh league title in 2012 but they ended the regular 2013 season in third place, behind Aktobe and Astana.
Schalke's Ukraine-born defender Roman Neustadter says Ukrainian football is on the rise after his club were drawn against Metalist Kharkiv.
"It's a nice, exciting draw for us," he said. "Ukrainian football has come on leaps and bounds in recent years and the euphoria there is high, particularly after the 2012 European Championships.
"The clubs have also strengthened and it's going to be a tight game.
"Personally, I'm looking forward to playing for Schalke in the land of my birth."
Elsewhere, Real Sociedad's reward for their impressive Spanish league campaign is a two-legged tie with French giants Lyon.
The ties are to be played on August 20-21 and August 27.