one trick for next time, is to make sure the tire ISN'T seated on the rim as you go for that last squeeze. Keeping the tire unseated, off the rim seat, in the middle of the rim, adds a few crucial mm's of difference.
I change a LOT of tires at the bike shop. the 'tire unseated' trick helps enormously. you should be able to roll just about any tire (except downhill) on without irons.
using a tire lever like a spatula works great. the quickstick is a great aid, and requires the 'spatula' method.