The 36-year-old's 62nd-minute tap-in lifted Di Natale past Gabriel Batistuta into 10th spot in the all-time Serie A scorers' chart.
"I'll try to reach Del Piero's total. (Francesco) Totti's number will be unreachable but the 188 goals scored by Del Piero is definitely doable," Di Natale told Udinese Channel.
Di Natale could see himself end his football career number seven in the charts, with Swedish striker Kurt Hamrin's total of 190 looking more than attainable.
He announced that he would retire at the end of the season after a 3-1 home defeat by Hellas Verona in January, a move that shocked the fans and manager Francesco Guidolin.
However, he said he was reconsidering that decision last week, and should he carry on next season he will almost certainly be looking at overtaking Roberto Baggio on 205 goals.
Di Natale is from Napoli in the south of Italy but has spent his entire football career further north, spending eight years at Tuscan club Empoli before moving to Udinese, who are close to the border with Slovenia, in 2004.
Many clubs have come knocking for him over the years including his hometown team, but he has always remained faithful to a provincial club that has never won a major trophy in its 117-year history.
Di Natale and Udinese are small in stature, but over the last decade they have both punched well above their weight.
"I've played in the Champions League, the UEFA Cup, two European Championships and a World Cup," Di Natale said last week.
"I could've won more elsewhere, but I made my choice and I do not regret it. I'd do it all over again."
Since Di Natale joined Udinese he has been Serie A top scorer in the 2009-10 and 2010-11 seasons, and last term he was the leading Italian goalscorer with 23 strikes as Udinese finished fifth and bagged a place in the Europa League.
This season has been less satisfying, but his goal on Saturday moved Udinese 10 points clear of the relegation zone and helped relax a tense atmosphere at the club.
"I've been here for more than 10 years. My family's here and I'm happy here. Everything I do is for this city," said the striker on Saturday.
"What we need to do now is get enough points for safety. If I happen to score goals as well I'll be happy."
- Sports & Recreation
- Antonio Di Natale
- Alessandro Del Piero
- Gabriel Batistuta