Gayle whacked an unbeaten 75 as the Windies posted a mammoth score of 205 to see off their opponents in Colombo.
"To be honest it was a slow track, but it was important not to panic," he said.
"I waited for the bad balls and when they came in my slot I hit them. Frankly we did not expect this big a total. We were looking at 140-150, but we got 50 runs as a bonus."
West Indies will now take on hosts Sri Lanka in Sunday's final.