When the visitors did threaten, in good spells at the start of both halves, goalkeeper Julio Cesar was equal to their best efforts.
Villas-Boas told Sky Sports: "We're a bit disappointed, but we'll take a point away from home and I think it's the first time we haven't scored for quite some time.
"The boys did well. We came out strong at the beginning and strong in the second half, we just couldn't keep the momentum.
"Maybe we didn't create as much as normal but we still take the point against a team that's just won away from home (at Chelsea) and is full of confidence.
"Julio made some great, great saves, and in the end they are decisive because if you score one it unlocks QPR.
"They're well organised, they defend well and can hit you on the counter, so to get that first goal was important for us. It's a pity we couldn't take those chances."