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.”
Colchester will hand late fitness tests to Ryan Jackson and Brandon Comley prior to their clash with Yeovil.
Arsenal secured their place in the quarter-finals of the Europa League following their 3-1 defeat of AC Milan at the Emirates Stadium on Thursday.
Danny Welbeck scored twice against AC Milan to toast his England recall by sending Arsenal into the last eight of the Europa League.
Ipswich striker Joe Garner will not play again this season after it emerged he suffered a fractured skull against Sheffield United last week.