Milan emerge from the weekend still top of Serie A, but with the gap to second place down to nothing, after rivals Internazionale won 3-0.
A stray arm by veteran Paolo Maldini literally handed David Pizzaro the chance to score the Udinese winner from the penalty spot, and despite playing for much of the second half with ten men, after the dismissal of Nestor Sensini, Udinese clung on.
Udinese's victory takes them up to sixth in the standings, but Spalletti insists that he will not allow his players to believe safety has been achieved already.
"What is our aim? The same as last week, and that of the week before - safety," insisted Spalletti.
"We must not think that after this win we can relax at all.
"Maldini's handball was pretty clear and I think we played very well in the first half.
"We maintained our rhythm and closed down Milan's space.
"We had to play more defensively in the second half because of our numerical inferiority.
"I don't want to comment on the red card, only on the performance of my players."
Milan coach Carlo Ancelotti was clearly upset by his team's lacklustre performance.
"It has been a poor match for us," said the former Juve coach.
"We attacked badly and it has been wholly negative for us.
"We had a lot of difficulty keeping possession and passing it around - of the 14 players that got onto the pitch not one played up to standard."
