Teun Koopmeiners put Juve in front after two minutes and Kenan Yildiz doubled the advantage after the half-hour mark in a dominant first half.
Lecce's Federico Baschirotto, however, pulled a goal back late on with a powerful header after Juve took their foot off the gas following the restart.
"We played a good game and after a ball lost by (midfielder Khephren) Thuram we got nervous," Tudor told a press conference.
"There is regret because we didn't finish the game well. We have to take this as a lesson."
Juventus kept Lecce under pressure for most of the opening 45 minutes, creating nearly 20 chances compared to three by the visitors.
The second half, however, was sedate by comparison until Lecce recovered the ball near the hosts' box and forward Ante Rebic saw his attempt brilliantly denied by Juve keeper Michele Di Gregorio.
But the visitors kept their momentum going and Baschirotto nodded home following a free kick in the 87th minute.
"Today I didn't like the substitutions," Tudor said.
"Football is no longer like it was before with the five substitutions. Today I didn't like how they came in. You have to grow quickly and everyone can have excuses, but in the end, the most important thing is the team."
Tudor made a triple change in the 67th minute, introducing strikers Timothy Weah and Randal Kolo Muani as well as defender Andrea Cambiaso, before Francisco Conceicao and Nicolo Savona joined later on.
Juventus moved provisionally up to third in the standings on 59 points before fourth-placed Atalanta, who trail them by one point, host Bologna on Sunday.
Juve next travel to 16th-placed Parma on April 21st.