Roberto Pereyra and Adam Masina scored in the first half for Udinese as Sampdoria fell to their 23rd defeat of the season.
"I feel enormous disappointment and sadness. We tried and we gave everything we had," Sampdoria manager Dejan Stankovic told DAZN.
"I know that every fan does not want to accept this day, but we fought on the field and they were by our side always. This club deserves more, because it is beautiful inside and out."
Marco Giampaolo was sacked as manager at the start of October, following a disappointing run of two points from their first eight games and the team's fortunes failed to improve following Stankovic's appointment.
"I tried my best and it was not enough. I am very disappointed and cannot find the words for how I feel right now," Stankovic added.
Sampdoria, who won the Scudetto in 1991 and have clinched the Coppa Italia four times, were last relegated in 2010-11, returning to the Italian top flight a year later.