The Giallorossi dominated at Marassi, but wasted so many scoring opportunities and were eventually beaten 2-1 in the final minute.
"In my view the right result should've been our victory," said Enrique. "I am happy with the performance, as we played well.
"Tonight the team played the way I want it to and I have to praise the lads. We've got to improve on many aspects, but this is my Roma."