You'll get stronger, don't worry. I think 20 mph is a bit high of a goal for a flat bar road bike, unless the bar is low & narrow, and the bike is light.

To me, a sustained 16 mph is a good pace on my drop bar cyclocross bike.

On my Simple City, I'm more like 14 mph.

Saturday, I was riding with a fellow bike forumer for around 30 miles. (barrettSCV) In the last couple of miles, he was leading on his titanium drop bar road bike at 22-23 mph on the flat. I drafted him and we kept this pace for a couple of miles. I couldn't have done it myself, but I could've done 20. But only for a couple miles. That is high effort stuff. For most of that 30 miles, we were going 16-17 mph. (no drafting, drop bar bikes) That keep the pulse pounding without being overkill for me. Again, with a flat bar bike, take off a couple mph. (unless the bar is low & narrow, in which case it comes down more to tires than the bar)

What width & tread pattern tires are you using?