Laurent Blanc’s side edged into a first-half lead after Adrien Rabiot broke the deadlock with a close-range finish after the 20-year-old was superbly picked out by Zlatan Ibrahimovic.
However, Chelsea responded before half-time after Costa slotted a cool finish past Kevin Trapp following a good counter-attacking move from the hosts.
The Spain striker was forced off in the second half due to an injury problem before Irabhimovic edged PSG into a 3-1 aggregate lead which meant Chelsea needed to score three times in the final 23 minutes to progress.
And former Chelsea manager Hoddle felt Costa’s injury and Ibrahimovic’s impressive performance were two of the key factors in the second leg of the last-16 tie at Stamford Bridge.
“I thought they were very composed in the way PSG played from the start and right the way through the game,” Hoddle told BT Sport.
“Ibrahimovic epitmoised that in the way he played and everything he did.
“A big loss was Costa coming off. Costa looked really good. Chelsea had a couple of chances where they might have gone 2-1 ahead.
“Costa got in behind a few times. You were thinking Chelsea might get something out of this game.
“As soon as Costa went off, you thought that was the end of it. It was a real top-class goal that knocked them out.”
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.
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