The midfielder insisted that the Ligue 1 leaders' season is not over yet, while former Chelsea defender Alex admitted the French champions are gutted with the European exit
The Ligue 1 champions had gone into the game leading 3-1 after last week's first leg at the Parc des Princes but a first-half strike from Andre Schurrle and an 87th-minute effort from Demba Ba saw the Blues progress on away goals.
Matuidi pointed the blame for PSG's defeat at their lack of European experience as well as the unavailability of talismanic forward Ibrahimovic through injury.
"We can be proud of what we have achieved," the France international told reporters. "We will learn from this match as we move forward.
"It was not going to be easy against a big team who have more experience than us. We had a chance to score, but the game swung in their favour.
"We were missing our top scorer Zlatan Ibrahimovic, which was a big loss. We're very disappointed. Now we must focus on other objectives for the rest of the season."
Meanwhile, former Chelsea centre-back Alex admitted that PSG were devastated at having exited the Champions League at the quarter-final stage for the second successive season, after what he admitted had been a sub-standard showing at Stamford Bridge.
"We conceded the first goal too easily and in the second half they started to put pressure on us," the Brazilian lamented. "I know how difficult it is for opponents to play here.
"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."