Leading 2-1 from the first leg of their last-16 tie, PSG appeared at real risk of blowing it when Jonas put Valencia in front on the night early in the second half.
However, Ezequiel Lavezzi's equaliser calmed the nerves and helped the French capital club go through, with a 1-1 draw ensuring a 3-2 aggregate win.
Ancelotti has won Europe's leading club competition both as a player and as a coach with Milan, so he knows what it takes to go all the way, but he admits that the performances of his newly put-together team have pleasantly surprised him.
"Nobody knows how far we can go," said the Italian.
"Up to this point we have done very well but this is our first year in the competition for a lot of the players.
"They have been fantastic so far, and now we will need to see what the draw brings."
Top of Ligue 1, and through to the quarter-finals of the French Cup, PSG are one of just a handful of European clubs still in with a chance of winning three major trophies this season.
Ancelotti says he is proud of that fact, even if his team's performances have often come in for criticism.
"We can't put all of our energy into Europe, because we are still fighting on three fronts," he said.
"Porto, Juventus and Bayern Munich are the only other teams in Europe still fighting on three fronts, so I am very happy with the team and I want to say thanks to all of the players."
Despite being deprived of Zlatan Ibrahimovic due to suspension following his sending-off at the Mestalla, Ancelotti opted not to hand a first Champions League start of the season to Kevin Gameiro, and PSG lacked any kind of reference point in attack as a result.
David Beckham, meanwhile, started on the bench and that was where he stayed for the night.
The first real chance of the game fell the Spanish side's way, with Roberto Soldado testing goalkeeper Salvatore Sirigu quarter of an hour in.
PSG were struggling to find any rhythm, and were disrupted even more when Christophe Jallet was forced off before the half-hour mark, seemingly due to an injury, with Gregory Van der Wiel taking his place.
But for all their dominance of possession, Valencia could not seriously trouble Sirigu, with Jonas and Tino Costa both missing the target before the Brazilian had a powerful shot beaten away by the 'keeper just before the interval.
For PSG, that served as a warning of what was to come, with Valverde signalling his intent by throwing on creator Ever Banega for midfield destroyer David Albelda at half-time.
He was rewarded for his positivity when Jonas struck soon after the restart, his powerful effort from 20 yards surprising Sirigu at his near post.
Suddenly a tie that had appeared to be limping towards a tame stalemate had come to life, and Ancelotti finally turned to Gameiro.
The striker, who Valencia had wanted to sign in 2011 when PSG lured him from Lorient, looked lively as soon as he was thrown on for midfielder Thiago Motta in the 58th minute, and he made PSG's equaliser on the night just before the midway point in the second half.
After driving through the middle of the Valencia defence, he got the break of the ball, but it was Lavezzi who shot, and then converted at the second attempt after 'keeper Vicente Guaita had blocked his initial effort.
It was Lavezzi's fifth goal in the Champions League this season, confirming that PSG do not rely solely on Ibrahimovic to score when it really matters.
Ernesto Valverde, the Valencia coach, was left to wonder what might have been after his side gave themselves too much to do by conceding twice in the first leg at home.
"The first leg had an impact on this game," he said. "This game was similar, with us having most of the ball, but we didn't allow them as many clear chances this time.
"We had to be tighter at the back but still try to win the game. Unfortunately we tired towards the end and that allowed PSG more opportunities."
Valverde acknowledges that PSG are a strong team but, when asked, he refused to say how far he thinks the French club can go in the competition.
"Now every side that is in the quarter-finals is strong," he added.
"I don't know how far they can go. They are a new team with a new coach. They are having a good season but now they can expect to face tougher ties.
"I'd prefer it if the question was the other way round and that it were us in last eight, not them."
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