Troy Deeney saw his spot-kick saved, but the Hornets extended their unbeaten run in the Premier League to seven matches.
But Mourinho told BT Sport afterwards: "I think we deserved to win this match. To lose would have been too harsh on the boys."
"The result is unfair. I think it would have been more unfair if we lost," added Mourinho, whose side have now gone four matches without a win.
"We had the control of the game, especially in the first half. We arrived in dangerous positions. We created chances but we did not manage to score."