Lazio's slim hopes of a Champions League spot remain alive and they now have a psychological edge as they prepare to face Juve on Tuesday in the first leg of the Coppa Italia semi-final.
They are seventh with 46 points, eight behind Bologna, who occupy the fourth Champions League spot, with Thiago Motta's team scheduled to face bottom club Salernitana on Monday.
"It is wonderful to win this way and we could not have started this experience better," Tudor told DAZN.
"I am glad for the players, the way they interpreted the match and to have started on the right foot."
Despite securing the win with a stoppage-time goal by Adam Marusic, Tudor dismissed the notion luck was on Lazio's side.
"We train hard and what happens on the match day is a consequence of what we do during the week in training. We want to have no excuses," he said.
Tudor started with Ciro Immobile on the bench, the veteran striker having also been left out of Italy's squad for their recent friendlies.
"Immobile knew that it was only right (Taty) Castellanos starts when he scored two goals in the last game," Tudor said.
"I am here to motivate the players, but they need to give me determination. I saw Immobile hungry, he wants to get the best out of these two months and I am glad about that."
