Alessandro Matri drew first blood for Juve but the hosts were pegged back by an equalizer from Antonio Floro Flores before Matri doubled his account with the winner in the 62nd minute.
"I was very concerned about this match because Udinese are a team that play attractive football and have a lot of quality players who function as a great team," Conte told Sky Sport Italia.
"In the end we paid a small price of fatigue from the Coppa Italia, but still earned a major victory. We need to improve our grip on a match, as today we lost too many balls in midfield, leaving too much space for Udinese to hit us on the counterattack."
Conte though, was impressed by the efforts of forward Emanuele Giaccherini with the latter arriving to Juventus last summer from modest outfit Cesena.
"[Giaccherini] is a player who has strength and technique, fits in between the lines well and times his runs superbly," Conte added.
"He is the example that even in the minor leagues you can fish for important players, who can benefit clubs like Juventus."
Juve are now four points clear of AC Milan following their victory although the Rossoneri are due to face Cagliari on Sunday.