Gustavo Manduca struck on 90 minutes to send 25,000 fans into raptures after Porto, who were surprisingly held 1-1 by APOEL in Portugal last time, thought they had grabbed a point thanks to Hulk's 89th minute penalty.
Ailton's 42nd minute spot-kick had given the impressive Cypriots the lead.
"At this stage we are very close to the Europa League and it seems we are going to play in Europe until March," the down-to-earth boss told reporters.
"As for the Champions League we will try to achieve it. It will be great but still we have a way to go. My wish is that my players will keep playing with the same passion in the remaining two matches. If we do it, and it is up to us, then we have chances to do many things."
"It was a complicated match. The first half wasn't well played. We had the will to win and put in many crosses but had few clear chances and ended up conceding," Porto coach Vitor Pereira told reporters.
"The second half was different, we created chances and made it 1-1. After that, a team with our experience, that won the Europa League, should have settled down and not got carried away emotionally.
"We should have used our heads more but we lost balance as a team and got punished," added Pereira.
"We still depend only on ourselves and must now win the next two matches to qualify."
Hulk then nearly scored from close range while a minute later the home side's Ailton had a diving header saved.
