Villas-Boas thinks had Spurs taken a first-half lead from the spot, that would have applied too much pressure on to Arsenal, who did not score until the 50th minute.
"I don't want to put the spotlight on the referee, but I think it (was) absolutely decisive," the Tottenham manager said.
"Apart from the distance that separates the grounds, the emotions are felt very strongly. It would have certainly been felt at Newcastle, and it would certainly change the running of this game too.
"Sunderland would have to be more adventurous, and so there would be more space."
Villas-Boas has repeatedly defended Bale this season amid accusations that he dives, and he thinks Andre Marriner got the decision wrong.
"It was extremely disappointing decision in my opinion for the fact that Andre was on the conference at start of season and we spoke about Gareth's incidents," Villas-Boas said.
"It was a poor decision. It could have potentially changed the nature of other game too."