Roma went into the game on Sunday having conceded only one goal in four rounds this season.
Roma defender Rick Karsdorp and goalkeeper Rui Patrício were at fault for the first two goals from Destiny Udogie and Lazar Samardžic. Roberto Pereyra and Sandi Lovric added to Roma's humiliation in the final 15 minutes.
"Individual errors are always group ones for me," Mourinho said.
"We have 10 points and a lot of teams are close. I want to congratulate Udinese, which was perfect tonight.
"I prefer to lose one match 4-0 than lose four matches 1-0. It's hard for us and for our fans, but that's life, there's another match on Thursday. That's what I told my players."
It was a third straight victory for Udinese and lifted it up to fourth, level on points with Roma.
"The guys were extraordinary tonight, against a really strong team and we also played good football," Udinese coach Andrea Sottil said.
"We have to keep our feet on the ground, we are aware of our strengths but we have to take it match by match, with hunger and humility against every opponent."
Mourinho's side was looking to move back top of Serie A but it gifted Udinese the opener with less than five minutes on the clock.
Pereyra floated a cross in from the right and Karsdorp chested it down toward his own goalkeeper at the back post, but he didn't realize that Udogie was right behind him and the teenager snuck in to prod home.
Udinese doubled its lead in the 56th minute when Patrício allowed Samardžic's snapshot from distance to squirm out of his hands and into the back of the net.
Roma almost grabbed one back immediately but Gianluca Mancini headed a corner off the left post.
The capital side fought desperately to get back into the game but left itself exposed at the back and Udinese sealed the result with two counterattacks.
One was finished off in the 75th when Jean-Victor Makengo laid the ball off for Pereyra to curl into the far side of the net. Seven minutes later, Pereyra turned provider to set up Lovric for his first goal since joining from Lugano in the offseason.
Cremonese picked up its first point in Serie A for more than 26 years with a 0-0 draw at home to Sassuolo.
Cremonese had started its first season back in the Italian top flight since 1995-96 with four straight defeats.
Hellas Verona recorded its first victory this season by coming from behind to beat Sampdoria 2-1, turning the match around on the stroke of halftime.
Francesco Caputo scored a stunning opening goal for Sampdoria five minutes before the break but Verona leveled four minutes later when Thomas Henry's header came off the crossbar and went in off the back of goalkeeper Emil Audero's head.
Scottish defender Josh Doig, a new signing, scored what was to prove the winner moments later.
Elsewhere, Marko Arnautovic scored two goals as Bologna drew 2-2 at Spezia.