The Ligue 1 table-toppers took the lead in just the 11th minute as Alassane Plea opened the scoring but they failed to capitalise and Enzo Crivelli levelled affairs for Bastia on the hour mark.
There were no further goals and Les Aiglons are now just one point clear of both Monaco and Paris Saint-Germain.
There is clearly no panic in the Nice ranks but Favre admitted that his charges had possibly switched off a little to allow the opposition to get something from the game.
"We scored quite quickly and then perhaps subconsciously we relaxed," he told reporters. "We played very well in the last 20 minutes and had chances to make it 2-1.
"I don't think there was a lack of willingness but we maybe took our eye off the ball a little in the 10 minutes after we scored and then after the break."