The Ligue 1 champion looked set to reach the semifinals of Europe's premier club competition for the first time in 19 years when the team secured a 3-1 first-leg lead at Parc des Princes.
The manner in which PSG was denied a place in the last four was hard to take for Laurent Blanc's side, but Brazilian defender Alex admitted the team came up short in Tuesday's second leg.
"We conceded the first goal too easily and in the second half they started to put pressure on us," he told reporters. "I know how difficult it is for opponents to play here [Stamford Bridge]. We didn't start with enough aggression like we played at home.
"Scoring the first goal near the end of the first half was very important for them.
"It was very difficult for us and all the players are sad. We were confident of getting a good result but we did not play like we can and we paid for it."