PSG left it late at GSP Stadium, with striker Edinson Cavani scoring with three minutes remaining to snatch a 1-0 win in the UEFA Champions League.
The Group F leaders were expected to stroll to victory - despite injured Zlatan Ibrahimovic on the sidelines - but Cypriot side APOEL frustrated the visitors throughout, threatening to score on a couple of occasions.
But PSG took a giant step towards the knockout rounds, with the French champions a point clear of Barcelona after three matchdays.
"My players didn't give up and kept fighting right until the end," Blanc said post-game.
"It could have gone either way but we were fortunate to take the three points.
"My team were positive on the pitch. We played against a good, organised, defensive team but also one that is dangerous and could have scored.
"It's not for me to say whether or not we deserved the win but I can say that it was important for us to get three points."
Blanc added: "APOEL are a very well-organised team. If you don't score early against them, you can be sure you will be in for a difficult evening.
"Our performance was not the best and this is certainly not a game that will be remembered for how great we played. But we will happily take the three points and look ahead."
Blanc hopes Cavani's 87th-minute winner will help kick-start his season.
"Cavani scored to give us the win so I am obviously happy with that," said the Frenchman.
"He has been lacking some confidence of late and this goal will hopefully help him for the future."
The Uruguay international, who has been constantly linked with a move away from the French capital since leaving Napoli in 2013, added: "The most important thing for a striker is to score.
"And the most important thing for Paris tonight was to take a step closer to our first objective of the season: making it to the knockout stage."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.