It was the fourth time Avram Grant's team had surrendered the lead in the final seconds of a home game. Aston Villa, Everton and Wigan also scored late goals to earn a point.
"Losing those eight points has been massive for us," said Drogba. "It is far too many for us to lay claim to being champions. It is certainly proof of too much complacency and a lack of concentration on our part.
"Each time we had the result in our hands but sometimes we mentally finish games before the final whistle.
"Manchester United deserved their title. They have been rewarded for their consistency. We have made too many mistakes, including on Sunday when we let Bolton equalise 30 seconds before the end of added time."