Victory would have seen Les Parisiens effectively clinch the Ligue 1 title, but they will get another chance to seal glory against Lyon on Sunday.
Silva received his marching orders just before half time whhen his team were trailing to Gael Danic's 17th-minute strike.
The hosts rallied back and Brazilian centre-back Alex grabbed an equaliser seven minutes from time to claim a point.
"We are disappointed because everyone was hoping for victory this evening," Ancelotti told reporters. "At the end of the day, this point we earned with just ten men is not that bad, and we probably deserved to win given we played so long a man down.
"When we were reduced to just 10 men, the team showed really great character and a great spirit in the second half. I'm very happy with the team's performance after an opening 45 minutes that really weren't very good.
"We still need to win one more match and try and win the title in Lyon next week. It's going to be a huge match."
PSG will be crowned champions if Marseille fail to beat Toulouse on Saturday.