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.
Former Arsenal defender Dixon felt PSG dictated the second leg of the last-16 tie at Stamford Bridge.
“Chelsea worked hard but came against a good side in PSG,” Dixon told ITV Sport.
“It always looked like the tempo of the game was set by PSG as opposed to Chelsea. They’re a good side.
“I still think they’re a little bit below the top sides like Barcelona and Bayern Munich.”
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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