Frank Lampard nodded home a 50th-minute cross from Branislav Ivanovic but the visitors were forced to hang on with Ivanovic heading against his own crossbar with four minutes to go.
"We are very happy because we needed this stimulus of a win before the international break to make sure everybody goes into the break with a better feeling," Villas-Boas said.
"It (the clean sheet) was important. It is always important to win the game, no matter what are the conditions. We had to suffer a little bit but we managed to hold onto a clean sheet.
"It is never easy at Ewood Park, particularly when you are going through back-to-back defeats in the Premier League and bearing in mind that Blackburn are in desperate need of points."
Rovers boss Steve Kean claimed not to have noticed a small plane which buzzed above Ewood Park in the first period trailing a banner reading 'Kean Out'.
Kean also shrugged off a small post-match protest and instead chose to hail another fine performance from his team who could have taken at least a point.
"I don't feel let down because I think my players gave it everything," he said. "We are disappointed not to take anything from the game after creating that amount of chances.
"I feel like we should have taken at least a point but the overall performance not only in this game but in others recently has been excellent.
"Yakubu had some chances on the counter-attack and we are creating those chances. The strikers have just got to keep in there and we have lots of young lads who have given sterling performances."
Source: PA
Source: PA