Never ever say this in a professional realm. I have heard it time and again (and have even used it without realising the kind of image I was projecting). It’s a horrendously misleading phrase and it creates more of a negative connotation than a positive one. If you are required to finish 5 reports and you finish just 2 of them, you can say ‘I did my best’ (and you probably did) but did you complete your task? No. By no means. Don’t say you will do your best because your best may not be enough!