Valencia scored in the second half through Adil Rami in order to level the scorelines after Ola Toivonen gave PSV an early lead in Eindhoven. Rami was sent off later in the match, however, as the French defender collided with Toivonen in the 88th minute.
PSV were one of the high-scoring sides in the competition having scored 22 goals until the round-of-16 match. Valencia had earlier played out a high-octance 4-2 win at the Mestala last week and were thus wary of the Dutch outfit in the return leg.
"We are satisfied to reach the quarters and also satisfied with our attitude, because we were firm and we played safe," Emery told EFE.
"We had a lot of respect for PSV. We knew about their attacking potential and they had a lot of chances to score, though we also showed clarity when we went out to attack."
"We could not possess the ball enough to do them more damage, but the draw also gives us the feeling that we played seriously."
The 40-year-old was also annoyed by Rami's dismissal as it occured through an off-the-ball incident. The referee had initially given a penalty but upon consultation with the linesman, he relented and gave a free-kick instead.
"Although Rami was provoked, it is a shame that there was no self-control because we have discussed and worked this during the season," Emery commented on his player.
"We cannot allow (a player to make) such actions.
"In Europe, these actions do not go unpunished. What he did was reprehensible and we cannot allow things like this."
Emery's future at Valencia is also currently in doubt as the club, well-placed to achieve a consecutive third-place finish, have not always seen eye-to-eye with the coach.
The former Almeria manager had released a book in February called "Winning Mentality: The Emery Method" and it was poorly received by the fans. The Association of Valencia Supporters Club said in a letter that the fans were "disgusted" with him and believed that his team lacked "commitment, courage, dignity and identity".
The manager also reportedly criticised his players for their attitude towards training earlier in the season.
Furthermore, midfielder Tino Costa had recently retweeted an angry comment by a Valencia fan towards the manager but he later claimed that it was not intentional.