Douglas Maicon struck twice for Inter, though his winner was clearly offside.
"I am not surprised by Siena's performance and I must say we did not deserve to win this match. I don't say that because our winning goal was offside, as this is part of the sport," said Mourinho.
"[Hernan] Crespo was also flagged offside incorrectly when he was clear on goal and who knows what would've happened then. I say we didn't deserve to win because Siena played extremely well. They are very organised, keep intense pressure on the ball and made it difficult for us to play.
"Their counter-attacks are very tricky and they always swarmed in with three or four players ready for the cross. I complimented [Coach Marco] Giampaolo after the match and promised him I'd repeat the phrase I said to the media, which is 'well done, you did not deserve to lose.'"
Siena were until now unbeaten on home turf this season and had not conceded any goals from open play.
"I was aware of the difficulties of this match. [Mario] Balotelli and [Luis] Jimenez hadn't played in a long time and [Dejan] Stankovic was suspended, as he is crucial at the moment.
"If Jimenez doesn't play when the team has a diamond midfield and Stankovic is suspended, then when will he play? At times I prefer to run a risk and boost the self-esteem of my players. I don't think he played badly, he was just lacking that match tempo against a very aggressive opponent."