Yes, road bike tires and mtn bike tires are basically the same. Carry a spare tube, patches and glue, tire levers and a pump. Or read this article for leverless tire changes:

http://www.teamestrogen.com/articles/asa_levers.asp

Most importantly, practice changing tires at home before you have to do it on the road. IMO, if your tube is blown and you are going to junk it anyway, go ahead and use tire levers with impunity to remove the tire. If you want to salvage the tube, avoid the levers or use them carefully to remove the tire. Avoid them altogether when replacing the tire. But expect sore thumbs. Narrow road bike tires can be difficult. But you won't hurt them. They can handle 100 psi - more force than you could generate.