A few people have touched on this but you can partly blame the lack of quality on the ball (remove Fernandes) as well as Ole's desire for us to play the ball out from the back.
Our backline, with the exception of Maguire, are very average at playing out from the back. Any team that deploys a high press will force mistakes, and we've seen this kind of thing happen with alarming regularity over the past couple of seasons.
Put quite simply, we lack the all round quality to play through a side, unless we can beat the first press and get it into Bruno.
Ole probably knows this, but if that's the way he wants to play, he'll probably be willing to fall on his sword in doing so.
He is clearly looking to develop us to be more than just a counter attacking side, but he doesn't really have the calibre of players to pull it off as yet, certainly not against sides who press high (Bournemouth and Southampton caused us problems, it would be rude not to expect Chelsea to do likewise).
Its easy to see...watch how many touches the likes of City and Liverpool take when they look to play through a side.
We take at least 3 times as many, by which point the door to Rashford and co has been closed, player in possession takes another touch, and all of a sudden, we have lost the ball in our defensive third.
I fully expected us to deploy a similar strategy today, as neither of Chelsea's CB's are good on the ball. However, Lampard recognises this, so most things went long up to Giroud with support getting around him to pick up the pieces. Not pretty, but ultimately effective.