The Ligue 1 champions broke the deadlock in the 16th minute after Adrien Rabiot finished from close range after Zlatan Ibrahimovic found the 20-year-old with a superb, low cross.
Tonight it sunk in just how far Chelsea have slipped behind the rest of Europe
However, Guus Hiddink’s side levelled before the break after Chelsea striker Costa escaped the attentions of Thiago Silva and finished past PSG goalkeeper Kevin Trapp.
The Spain striker was forced off in the second half due to an injury problem before Sweden captain Irabhimovic handed PSG a 3-1 aggregate lead thanks to a close-range finish.
Former Arsenal defender Keown believes Chelsea 2-1 loss to PSG highlights just how far the English champions have fallen behind Europe’s top sides.
“Diego Costa was really important and was giving the two Brazilian defenders a torrid time,” Keown told BBC Sport.
“When he went off the pitch so did their chance of getting through to the quarter-finals.
“Tonight it sunk in just how far Chelsea have slipped behind the rest of Europe.”
Chelsea make the trip to Everton on Saturday afternoon for their FA Cup quarter-final at Goodison Park.
The defending Premier League champions are in tenth place and 10 points behind fourth-placed Manchester City in the race to secure a place in next season’s Champions League.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news