A pressure canner will be required of course but even then they can't be in gravy - depending on what you mean by "the gravy". Gravies have thickeners like flour and such in them as well as the fats from the meat juices.

Just can them plain per the instructions below with a 1" headspace and then add them to the roast for the last 30 mins. or so.

Dave

Here is a link that might be useful: Canning carrots

I would use beef bouillon instead of salt in the standard carrot recipe. This will give you a similar flavor to what you get with the pot roast gravy.

Jams and jellies only need a water bath (if that) but this will require pressure canning.