The 26-year-old kicked over 14 points at the Aviva Stadium in what was the first appearance for a Scottish side in the last four of the tournament.
"It was a tough game," he told BBC Sport. "We just fell off a bit in the second half.
"We're extremely proud of where we've got to. We came to win today. For a lot of our team it is their first year in pro rugby - they can hold their heads up very high."
Ulster will take on either Clermont Auvergne or Leinster in next month's final at Twickenham Stadium.