Last summer I did a few mountain ascents in the rockies for the first time, and found it a very different experience than the sharp bluff climbs we get here in Minnesota. I like your question, because for me it was mostly a mental challenge, and much less about leg muscles (although they are pretty important).
One thing that helps me is to use the same thought that helps me shovel out from a heavy Minnesota spring snowstorm: every little shovel full is one step closer to being done, so just think about what's in the shovel now, and not worry about how much is left to shovel.
On a pass climb, I tried to avoid looking too far ahead, and worked on a sustainable pace, even if it was only 3 or 4 miles an hour. Eventually I got to the top, and then I looked down to the valley, and just like a shovelled driveway, said to myself, "I did that?"