Brendan Rodgers is receiving lessons but has yet to master Italian. The same can be said of his Liverpool team as another performance high on entertainment, possession and promise could not prevent a 13-match unbeaten European run at Anfield ending against Udinese. It was enough to provoke the first public rebuke of the Liverpool manager's reign.

Fiorentina were the last visitors to triumph here in Europe, in the Champions League in December 2009, prior to the pertinent reminder from Udinese that the only statistic that counts is on the score sheet.

It was not the re-emergence of an Italian problem that troubled Rodgers, however, as the flaw that has undermined too many encouraging displays this term. Liverpool dominated the completed passes by 691 to Udinese's 173. They enjoyed a possession rate of 77.9% in the first half. But their defending rendered the positives redundant. A lack of concentration and yet more individual errors have changed the complexion of Group A following the high-scoring and also error-strewn win over Young Boys in Berne.

"We totally dominated in the first half and some of our play was very good but we were so loose at the start of the second half it was frightening," said Rodgers. "Our concentration was very poor and, before we knew it, we were 3-1 down and chasing the game. We had a good final 20 minutes but it was too late by then.

"I thought we were lazy. We were loose, lazy and sloppy. Simple as that. It is a lesson – you have to earn the right to win the game but we didn't do that at the beginning of the second half. Maybe we thought the game was too comfortable but at this level it never is. We need constant reminders and constant work that you have to maintain concentration and earn the right to win. You can't keep having to score two, three or even five goals just to win a game."

Udinese's senior players had appealed to their coach, Francesco Guidolin, not to deny them an appearance at Anfield and the striker who led the requests, Antonio Di Natale, repaid him with a superb display. Liverpool, as is Rodgers's wont in Europe this season, were much changed but on course for a repeat of the encouraging wins in Berne and at West Bromwich Albion in the League Cup until losing their way completely in the second half.

José Reina made his 80th appearance for Liverpool in Europe, equalling the club record for a goalkeeper set by Ray Clemence, but his momentous night was spent in an increasingly agitated state at the lack of protection in front of him. The Liverpool goalkeeper made a stunning first-half stop to prevent Mehdi Benatia glancing Di Natale's free-kick into the bottom corner. He was powerless as Udinese transformed the tie at the start of the second half.

Guidolin had to inject urgency into a passive Udinese performance at half-time but he must have been astonished by the impact his substitution made. Just 35 seconds had elapsed in the second half when the substitute Andrea Lazzari seized on a Glen Johnson mistake. Roberto Pereyra took over and found Di Natale, who picked out Lazzari's run into space down the left and then ghosted into the area to stroke the return beyond Reina with a fine first-time shot.

Lazzari engineered Udinese's second with an inswinging free-kick that Sebastián Coates inexplicably headed past his own goalkeeper. Two minutes later, a flowing Italian move saw Di Natale hold the ball up inside the Liverpool area before laying it off for Giovanni Pasquale to drive an unstoppable left-foot shot into Reina's bottom corner. "Di Natale is quality, there is no doubt about that," said Rodgers. "But we gave him too much time to juggle the ball in our box."

Liverpool had deservedly led through a Jonjo Shelvey header. The midfielder, sent off against Manchester United on his last outing, started the move with a ball out to Stewart Downing on the right and sprinted into the box for the return. Downing delivered to perfection and so did Shelvey with a header guided beyond the despairing dive of Zeljko Brkic.

It took the defensive collapse to spark Liverpool into a sustained threat in the second half, however. Luis Suárez, on as part of a double substitution with Steven Gerrard, reduced the arrears with a stunning free-kick. He was also denied twice at close range by Brkic and once more on the Udinese goalline by Shelvey when the striker's half-volley beat the keeper only to hit his own man and rebound to safety.