I never thought I'd win the prize, but I'm happy I got to make a run at it.
Did I win the prize or not?
Thanks
PBF
I"d say no.
If you did.
I never thought I'd win the prize. I was just happy I got to make a run for it.
That is, first you were happy that you got to try. Now you are happy that you won. So, the "happy about trying" part goes into the past tense.