Thiago struck a second-half brace and set up another in Bayern's huge win in the first leg of the Champions League last-16 tie at the Allianz Arena on Wednesday.
Ancelotti praised the Spanish midfielder for his performance as the Bundesliga giants took a huge step towards the quarter-finals.
"He played very well and scored two goals," the Italian said.
"It was a perfect performance."
Arjen Robben put Bayern ahead before Alexis Sanchez levelled for the visitors, tucking away an equaliser after his penalty was saved.
But Ancelotti's team dominated the second half as Thiago struck twice to go with goals from Robert Lewandowski and Thomas Muller.
"The result is important, but we have another game in London," Ancelotti said.
"We need to show the same passion."
The second leg is at Emirates Stadium on March 7, with Arsenal on the verge of making a last-16 exit for the seventh straight season.