PSG fought back from 2-0 down to draw level with two goals in the final ten minutes to take the tie to penalties, which they won 4-3.
Afterwards, Frank said in Udine: "Very, very proud of the players, the team, the club, the fans. I think the players gave everything, playing against one of the best team in the world, maybe the best, at the moment, and I think we were 75, 80 minutes perfect, almost giving nothing away against, they had four players with unbelievable individual quality on the pitch. So very, very proud of them.
"It’s down to the smallest of margins in the penalty shootout. It’s like the flip of a coin. First I’d like to thank all the players that stood up and were brave and took responsibility to take a penalty."
I don't know what happened
On those two PSG goals in the final ten minutes, Frank also stated: "I wish I knew. I think sometimes football is the smallest of margins. They kept pushing, made some subs that put us under pressure at times. But it’s a shot from the edge of the box - before that we didn’t concede really any big chances.
"I think there was one save from Vic where he needed to save it. Then the momentum built and they scored - of course they had some crosses, some situations, and we need to dig deep. But it’s basically the next chance, it’s not like they have three chances before this goal. Small margins, small margins."
Frank was also asked about the importance of the Super Cup, something he insists should be regarded highly in England, just as it is across Europe.
He added, "I think every game matters. I think if you look on the face of the players and all of us, we are hugely disappointed and I have my rule for 24 hours. I can be disappointed for 24 hours.
"We want to compete in a lot of different tournaments and if you want to do that, you need to be ready to do a quick turnaround and go again. I’ll make sure the players are ready and come flying out on Saturday."