PSG appeared well set to reach the quarter-finals after a 4-0 win in the first leg, but a 6-1 defeat in the return at Camp Nou saw them crash out of the competition in dramatic fashion, with Sergi Roberto's winner coming deep into stoppage time.
Emery joined PSG at the start of the season and was tasked with bringing European glory to the Parc des Princes after the club failed to make much of an impact in the Champions League under Laurent Blanc.
It had been suggested their inability to reach the last eight - and the manner of the defeat to Barca - could have serious implications for the Spaniard but Al-Khelaifi insists there will be no knee-jerk reaction.
"After such a failure, everyone has to take their responsibility," Al-Khelaifi told Le Parisien.
"That includes me as the president, the sporting directors, the coach and also the players.
"Ever since he arrived, Emery has worked incredibly hard every day to help this team forward. We have to learn from this defeat and not let emotion dictate our actions.
"I have had some long talks with the coach in the past few days. Unai has a lot of quality and we believe in him. He has my full support and that of everybody else. We will discuss what changes we need during the pre-season. Everybody said he was the best coach in the world after the first leg. He has not all of a sudden become the worst coach now.
"Let's be serious, we have important goals ahead of us. We all have to turn our focus toward our remaining goals now."