But Mourinho told BT Sport afterwards: "I think we deserved to win this match. To lose would have been too harsh on the boys."
Watford goalkeeper Ben Foster saved from Lucas Moura before half-time to thwart Spurs, who have now gone four league games without a win.
"The result is unfair. I think it would have been more unfair if we lost," added Mourinho.
"We had control of the game, especially in the first half. We arrived in dangerous positions. We created chances but we did not manage to score."
Watford manager Nigel Pearson: "It was a game we felt we created enough to win. They have had their situations and chances as well. In the first half, we did not quite get our pressing as well as we have at late. We grew into the game and started to take more control. We had a good chance to win."
On the penalty miss: "It's football. I said to the players I am looking for a performance and we had a good performance today. If we go out with every intention to win the game then we will play well. I am pleased with how we played football today."