Gennaro Gattuso said it was "embarrassing" for Napoli to be seventh in the Serie A table, after taking over from Carlo Ancelotti as coach at the Stadio San Paolo on Wednesday.
Ancelotti was sacked as boss despite taking Napoli into the Champions League last 16 with a 4-0 win over Genk on Tuesday.
Gattuso left AC Milan at the end of last season after failing to qualify for the Champions League.
"The aim is to recoup points and get back into the Champions League positions," said Gattuso, who won the 2006 World Cup as a player with Italy.
"We need to work hard, win back points and come through this tricky period.
"It's embarrassing to see Napoli where we currently are in the table."
The 41-year-old replaces a friend in Ancelotti, who coached Gattuso to two Champions Leagues and one Serie A title over eight years in charge of seven-time European champions Milan.
"Ancelotti is like a father to me," he added. "He's always been close to me and supported me. He's won it all and I still have a lot to prove."
Former Rangers midfielder Gattuso joins Napoli at a difficult time despite their arrival in Monday's draw for the knockout stages of Europe's top competition.
Last season's Serie A runners-up sit 17 points behind league leaders Inter Milan.
More worryingly they are eight behind fourth-placed Cagliari, who hold the final spot for next season's Champions League, and have been engulfed in a row between the players and owner Aurelio De Laurentiis.
De Laurentiis ordered the players into a week-long training camp after defeat by big rivals Roma early last month -- a decision with which Ancelotti publicly disagreed -- but they rebelled and were hit with a massive fine that incurred the wrath of players' union FIFPRO.
"This team has what it takes to finish in the top four," insisted Gattuso. "The team is aware of the difficult situation and wants to do well. I've been encouraged.
"I fear nothing. I know I'm going to be working with experienced people. I hope to get results."
Gattuso signed a contract extension with AC Milan in April, but left the San Siro after they could only finish fifth in Serie A, missing out on a first Champions League campaign since the 2013-14 season.
Media reports in England suggest both Arsenal and Everton are keen to hire Ancelotti, who has won three Champions Leagues as a coach, after sacking Unai Emery and Marco Silva respectively.