The North London outfit had to wait until the 86th minute before Gareth Bale found the net to secure all three points and deliver a boost to their prospects of Champions League qualification.
"It was difficult to break them down," the Portuguese told BBC Sport. "In the first half, Saints had the better chances, we managed to hold on to 0-0.
"In the second half we improved and were much better and created a couple of chances, because Southampton did ever so well. They kept the ball well.
"But we waited, had patience and then managed to score."
Spurs are now level on points with fourth-placed Chelsea.