The north London outfit had not claimed three points at the home of the Red Devils since 1989, but were leading 2-0 at half-time thanks to goals from Jan Vertonghen and Gareth Bale.
Despite second-half goals from Red Devils duo Nani and Shinji Kagawa, a Clint Dempsey strike ensured Spurs held on for a vital victory.
And Villas-Boas feels his players can be “proud of each other” after withstanding a second-half onslaught to hold onto a memorable win.
"We were tremendous today, the players put in the effort and intensity to get a result," Villas-Boas told reporters.
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"The first half was totally different from the second but we can be proud of each other.
"It was an electric first 15 minutes of the second half but you can see from the desire to hold on to such a historic result that we can count on each other to do big things."
Villas-Boas revealed that goalscorer Bale was close to missing the game after suffering from flu, in just one of a number of mounting injury concerns.
He continued: "Gareth was unable to train this week with the flu and [Gylfi] Sigurdsson has been ill the last two days, so the team are exhausted from the effort they put in.
"You have to give compliments to everybody on a special night like this but it doesn't stop here, we have so many important games to play."
The former Chelsea boss was also quick to call on his side to build on the victory in this week's Europa League tie with Panathinaikos, as well as in the following weekend's clash against Aston Villa.
"We go to [Panathinaikos] and we need a result to give us a strong position in the [Europa League] group, then we have Aston Villa two days after. It is important to continue from this."