"Inzaghi reached a great achievement tonight, proving he still has a lot of life left in him," said Ancelotti, after Inzaghi surpassed Gerd Muller's UEFA-recognised total with his 63rd goal.
The 1-0 victory over Celtic also allowed the Rossoneri to win their Champions League group, which will make them seeds in the knockout draw and give them the second leg on home turf.
"Today we played a relatively tranquil first half, but we stepped on the gas in the second. We have many objectives this season and it was important to top the group so we'd reach the next round with the right credentials. It is also a good boost for the Club World Cup."
Milan travel to Japan today for the tournament - previously known as the Intercontinental Cup - and they will enter from the semi-final stage on December 13.
"The European clubs have always struggled in Japan and we lost last time we were there," mused Ancelotti. "It is a great shop window for the South American sides and they seem to give a little bit extra. We have to prepare for this as we would a World Cup Final."