Saka had pulled a goal back to bring the score to 2-1 in PSG's favour on 76 minutes and was presented a golden chance four minutes later to draw level.
But Saka skied his effort high over the bar after meeting a cross from Riccardo Calafiori.
Keown later said on TNT: "It was painful and it will hurt Saka. He won't be sleeping for two or three nights. but he can be proud of his performance tonight. (Nuno) Mendes, we didn't see much of him in an attacking sense because Saka was on the pitch."
Rangers great Ally McCoist also said: "I'd love to have seen the last 10 minutes if Saka scored that goal. He should, but he just leant back. He got over it.
"It's a tap in. It's hard to be critical, but he's got to be sticking that in the back of the net and then we're in for a really entertaining 10 minutes."