United left Stamford Bridge furious with the manner of John Terry's late winner.
"We hate losing games and we know that we now have to go on a great run," O'Shea told MUTV.
"The international break comes at a bit of a bad time - you'd prefer to have another game a few days later to help put the defeat out of your mind. There's a bit of a sour taste left, but hopefully we'll get over that.
"Not many teams come to the Stamford Bridge and dominate games. We had great spells in the game where we had Chelsea really pinned back and we caused them problems on the counter-attack as well, but our final ball or shot just didn't go for us and we were lucky at times as well.
"We stuck to our game plan very well and were the better team.
"Unfortunately we didn't get what we deserved."