A few months ago, I also upgraded from a TriCross w/Tiagra triple to a Tarmac/Ultegra double.
On my TriCross, I rarely even touched my left shifter. Maybe when I rode it up South Mountain, or something big like that. On my Tarmac, I shift with my left hand rather frequently. It will take getting used to.
The only time I miss a triple is when I'm doing a big hill. I did South Mountain again a few weeks ago with my Tarmac. I thought I had run out of easy gears...but I had 1 left. You definitely don't want to jump into your granny gear too soon with a double.