The Parisiens lost 2-1 in the second leg of their last-16 clash with Real Madrid, as goals from Cristiano Ronaldo and Casemiro sealed a 5-2 aggregate win for the defending champions.
Draxler stepped off the substitutes' bench for the final 14 minutes at Parc des Princes but, with PSG already down to 10 men following Marco Verratti's red card, he was unable to effect the final outcome.
The Germany international was set to be introduced earlier, only for Edinson Cavani to make it 1-1 on the night in the 71st minute.
And Draxler has hit out at Emery for deciding against bringing him on at that stage and instead holding back despite needing two more goals to keep the tie alive.
"It was insensitive, " he said of the decision not to bring him on in the aftermath of Cavani's goal to ZDF. "I didn't know what was going on. I was surprised and angry.
"The goal for 1-1 went in but it did not change anything for us. I felt we needed to keep pressing and playing offensively.
"We lost a man, and even though we got it to 1-1 the whole stadium knew the game would not turn around because we didn't have the intensity on the pitch.
"Real Madrid played it out confidently and were not nervous at all."
The defeat marks the second time in two seasons that PSG have exited the competition at the last 16 stage, leading to increased speculation regarding Emery's future.
And Draxler did not hold back on his criticism for the former Sevilla boss, claiming the manager's failure to implement a more gung-ho approach despite trailing 3-1 from the first leg cost his side.
"We played the ball back and forth but you cannot score just doing that.
"You have to put pressure on Real Madrid when you are 3-1 down, not just pass it back and forth and hope something falls for you.
"We needed to put pressure on the opponents right from the start. We didn't do that so we deserved to be eliminated."
Draxler has become something of a forgotten man at Parc des Princes after PSG spent around €400 million to bring Neymar and Kylian Mbappe to the club last summer.
Their arrivals have not elicited a change in fortunes in European competition, however, leaving to Draxler to ponder that there remains something missing within the squad that will take them to the next level.
"In the summer we spent €400m and everyone was talking about how it was going to change things, but we have failed to get through this round again.
"I am still convinced this team has a lot to give, but you can see in games like this that there is still something missing if we want to win the big trophy.
"That should make us think again."