The Ligue 1 leaders squandered a 2-0 aggregate lead with just half an hour of the tie remaining, losing 3-1 in the second leg and 3-2 on aggregate thanks to Karim Benzema's hat-trick.
It means head coach Mauricio Pochettino could already be looking ahead to a change of scenery.
TOP STORY – POCHETTINO SET FOR PSG SACK AND COULD TURN TO MAN UTD
Mauricio Pochettino's job is "hanging by a thread" at PSG, according to the Telegraph.
It is claimed the Argentine can expect to leave the club at the end of the season following their Champions League collapse against Real Madrid.
Pochettino has long been linked with the Manchester United manager job and could now start to prepare for the prospect of taking over at Old Trafford.
ROUND-UP
- Cristiano Ronaldo has spoken with agent Jorge Mendes over his future at Manchester United, claims the Sun. Meanwhile, Bild reports the Red Devils are interested in signing Robert Lewandowski.
- Paul Pogba is another who could be leaving Old Trafford this year, but Juventus are not yet certain whether to try to re-sign him on a free transfer or offer a new contract to Paulo Dybala, Tuttosport claims.
- Barcelona are close to concluding an agreement with Chelsea defender Andreas Christensen, according to Sport.
- Arsenal want to sign two new strikers and a midfielder as part of a major squad overhaul, the Standard says. Alexander Isak, Dominic Calvert-Lewin, Jonathan David and Darwin Nunez are among the forwards being tracked.
- A consortium led by British businessman Nick Candy is working on a £2.5billion bid to buy Chelsea from Roman Abramovich, the Guardian reports.
La Real sold star striker Isak to Newcastle United last Friday in a club-record €70million deal.
That move happened quickly, with Sociedad president Jokin Aperribay confirming the club had expected to keep Isak in this window as recently as the previous weekend.
"It has been a difficult week," he said, presenting Sadiq as a Sociedad player after his signing from Almeria was secured on Thursday.
"It's been a summer full of rumours. When a player's [Isak's] agent tells you on a Monday at 10pm that he's coming to San Sebastian with a club the next day, the first thing you think of is that they have an agreement between them.
"We had a week left and we thought about Real Sociedad; it was not the time to discuss too much but to take action."
He added: "On Sunday, we didn't think that Alex was going to leave; on Monday, we started the talks [with Newcastle]; on Tuesday, we concluded them; and on Wednesday, we started working on the signings."
Fortunately, La Real had a plan, having first fielded interest from Newcastle in Isak earlier in the window.
"We thought we were going to sign two players, which is what we had thought of in June," Aperribay said. "We thought of Sorloth on loan and Sadiq to replace Isak.
"We started those conversations, first with Leipzig and then with Almeria."
Sorloth, who had spent last season on loan at Sociedad, scoring four LaLiga goals alongside Isak, quickly returned on another temporary deal.
But the €20m move for Sadiq took a little more time, concluded after "an intense 48 hours".
Now, though, Imanol's side are in a position of strength, having made a huge profit on Isak while bringing in a player in Sadiq who scored 38 goals across two seasons in the second tier with Almeria and has already added two in three games in LaLiga this term.
His signing was crucial, as fellow attackers Carlos Fernandez and Mikel Oyarzabal remain out injured.
"We had to be aware that when you come out of an injury you don't go from nought to 100," Aperribay said. "We have to support the youngsters and be patient with Carlos and Oyarzabal. That's how we approach the season."
He added: "Sadiq was the first on the list. We knew that with Isak we had a risk that became a reality last week, and we have acted as planned."
