After Matthijs de Ligt put Juve on track to seal the Serie A title, relegation-threatened Udinese fought back.
Ilija Nestorovski equalised before Seko Fofana scored a dramatic 92nd-minute winner, leaving Juve six points clear with three games remaining.
Sarri lamented his side's fatigue amid a busy run of fixtures, after their sixth game already this month.
"In this period, we are physically and mentally tired, and it is a problem common to all," the Juventus head coach said.
"For this reason, being aggressive is something more tiring and, therefore, now what matters most is order, because the inertia of a game changes very easily.
"It is difficult to keep it throughout the match and sometimes, like today, we lose it."
Juve will instead get a chance to secure a ninth straight Serie A title when they host Sampdoria on Sunday.
"At the moment I am not thinking about the Champions League, in my mind there is only Sampdoria and Sunday's match," he said.
"We have to be on the ball and then we'll think about the cup."