Ancelotti left the former England captain, who joined in January on a five-month deal, on the bench when qualification was at stake.
PSG, who won the first leg 2-1, qualified 3-2 on aggregate after Ezequiel Lavezzi salvaged a 1-1 draw at the Parc des Princes when he cancelled out Jonas's second-half opener.
Beckham started warming up at the end of the first half and continued during most of the second but after Valencia opened the scoring through Jonas, it was striker Kevin Gameiro who came on as a replacement for midfielder Thiago Motta.
"I hesitated between Beckham and Gameiro but I preferred Gameiro to add offensive energy and then use (Clement) Chantome as a defensive midfielder," Ancelotti said.
Beckham, who made his Champions League debut in the 1994-95 season when PSG last reached the last eight, is looking to make an appearance in Europe's top club competition with his fourth team after playing for Manchester United, Real Madrid and AC Milan.
He has made three appearances for PSG, starting one game, a 2-0 French Cup win against arch-rivals Marseille at the Parc des Princes last week.
Competition in midfield, however, is fierce at PSG, who have Marco Verratti, suspended on Wednesday, Italy's Thiago Motta and Chantome as well as France international Blaise Matuidi.
"He (Matuidi) is one of the best midfielders in Europe right now," Ancelotti said.
"At the 75th minute, he asked me to be substituted after he took a knock. I said no, you stay on the pitch," the Italian added with a smile.