Gareth Bale charged down Wigan keeper Joel's clearance to give Spurs the lead before goals from Emmerson Boyce and Callum McManaman put the home side in front.
However, Boyce's late own goal earned Spurs a point and the visitors, who are chasing UEFA Champions League qualification, could even have pinched the win after Bale and Tom Huddlestone were both denied by Joel.
When asked if he had feared the worst towards full-time, Villas-Boas told Sky Sports: "Towards the end, I was fearing the best to be fair!
"We had some good, good chances to make the score 3-2 and there was open football from both teams when we scored at 2-2.
"Before we scored, we were having difficulty breaking them down. We thought the first half was so good that, if we kept on moving the ball well and creating chances, we could have won the game.
"But credit to them, they fought very, very hard. They were well organised at the back and were shutting down all the spaces."
The draw leaves Spurs outside the top four on goal difference, with a potentially decisive meeting with Chelsea on the horizon next month, and Villas-Boas wants his players to continue demonstrating the same spirit.
The Spurs boss added: "When the 2-2 happened you saw how both teams were attacking each other and it was an open game which could have fallen to either side.
"The spirit is there to try to get this objective that we have."