Dominik Szoboszlai's free-kick in the first half put Liverpool ahead but the points would be shared after Richarlison struck in the 90th minute.
Asked for his initial emotions of earning a first point as Spurs manager, Tudor replied: "Nice! Nice, some fresh air, some good things for the confidence of the players, everyone again around the club and especially the fans.
"Good team spirit, seeing the circumstances the team was in today, coming here at Anfield with 12 (outfield) players, what we already know.
"So this is something big. We stayed in the game, we believed, I felt that we could score the goal, the players also felt it, so, ok, it's nice."
Tudor continued: "Yeah, yeah (we can build on this), we hope, you know. It's a long way to our goal, which is to stay in the Premier League, still a lot of games to play, but today was important to show what they showed, independently of the result.
"When you are honest, you need to be honest, give everything, then the football will give you back.
"That was my words before the game, so this happened today. As I said, it was not easy, and now we need to see now what to do in these two games, in front of us, to see who is able to play, who is not able to play, who is injured, who is not injured, so it's not easy. We continue to have problems from that point of view, the numbers, but that's why this result is even more important."