The Friuli outfit won 2-0 at Catania in Sunday's finale to edge Lazio into the vital third position.
"This is a great satisfaction for a small club like ours and for our city," Pozzo said. "We have 20% less capital with respect to other clubs.
"I have to congratulate our coach and our players for the results achieved in the last two years."
For the second consecutive year, Udinese took the last qualifying spot away from Lazio.
Sunday's triumph was Udinese's 18th win of the campaign and saw them finish on 64 points, two points clear of their closest rivals.
"I am happy because we managed an historic achievement at the end of an extraordinary campaign," Udinese coach Francesco Guidolin said.
"I thank my players. Nobody expected this and that perhaps made it even better than last year.
"The credit goes to my players, who overcame even the difficult moments."
Udinese captain Antonio Di Natale could not hide his delight as the experienced forward finished for a second consecutive year as the leading Italian scorer in Serie A.
Di Natale scored 23 league goals this campaign to propel Udinese into the top three.
"This is a splendid result for us," he said. "We conquered the Champions League for the second time in a row, overtaking teams like Lazio, Napoli and Inter Milan.
"We finished ahead of them in the table because we deserved it and did better.
"It is a great achievement and we must celebrate it.
"I am happy with my campaign."
The 34-year-old was on Sunday night included in Cesare Prandelli's 32-man preliminary squad for the Euro 2012.