Spurs had been without a victory this season before they managed a 3-1 win over the newly-promoted side at the Madejski Stadium on Saturday, with Jermain Defoe netting twice, with speculation increasing over the Portuguese's job security.
However, when asked if he was feeling extra pressure going into the game with the Royals, the former Chelsea boss replied to reporters: "No, not at all.
"I am extremely happy because the players put tremendous commitment into the game, [as well as] responsibility and concentration. They understood that we've been working so hard and they deserved to get this first win.
"The way they came into the game with that focus and wanting to put things in their place is very pleasing to see."
A number of the north London club's summer signings put in good displays to help Spurs claim the victory, with Mousa Dembele making his full debut, and Jan Vertonghen and Gylfi Sigurdsson also starring.
However it was Defoe who made the biggest contribution by scoring twice, though he should have had a hat-trick, as well as creating dangerous opportunities for his team.
"[I'm] extremely happy for him, he's such a prolific striker for club and country," Villas-Boas added. "He's amazing at sniffing goalscoring opportunities not only makes the most out of small opportunities that he has, he creates a lot for himself.
"I'm happy for him of course, there are questions being raised about him being played up front on his own and it being difficult for him. On his own or with [Emmanuel Adebayor] on his side I think Jermain can continue to produce attacking opportunities.
"Jermain deserves to be in this position because of what he has been doing in training, obviously when we started the season Adebayor wasn't with us.
"Jermain played again Newcastle, and scored, he then kept his place against West Brom and always creating opportunities for his team, and scored for his country once again. This helps the confidence of the striker and we're very grateful for [this]."
Tottenham's next match sees them face Lazio in the Europa League, something that the 34-year-old is looking forward to and taking very seriously, indicating they are aiming to go all the way.
He added: "[It's] very important because we want to do something special in this competition. It's a very very hard competition. You have to play, I think, 15 games before you reach the final. The worst teams of the Champions League come back, and sometimes we are talking about the best teams in the world.
"It gives access to the European Super Cup, for me I always thought about it as a prestigious competition and I think it should be promoted like that."