Against much better opponents, I take the mindset of accepting that I'm an underdog and looking for a way to win. That means taking care to give them nothing when they come to the table, and trying to take my chances when I can get out. (Obviously we should be doing these things anyway, but the 'looking for a way to win' situation seems to give me more focus on them.) It works for me (in terms of playing well, not always winning - although I seem to win more than I 'should'), whether it works for you too might depend on your temperament.
Another thought: Instead of thinking of success as beating the guy and failure as losing, it's worth recognizing that success can mean playing well and giving the guy a hard time. In your situation, this is just objectively true, I think.
I once played an exhibition game against the UK's #1 ranked player, and though I lost, I played great. One shot in particular I was very proud of. I consider that experience overall a big success (albeit tinged with regret for blowing a chance to win).