In opening remarks at a Manhattan synagogue, Rabbi Elliot Cosgrove also said the Democratic senator had an "abiding awareness of his roots" growing up in Paterson, N.J.
Lautenberg died Monday at age 89.
Hundreds of mourners filled the 1,000-seat Park Avenue Synagogue attended by Lautenberg's widow, Bonnie Englehardt Lautenberg.
New Jersey Gov. Chris Christie, former Gov. Jon Corzine and Sen. Robert Menendez, D-N.J., were among the dozens of politicians present. Vice President Joe Biden and former Secretary of State Hillary Clinton eulogized the senator.
Biden spoke of Lautenberg's decision in February to retire.
"It's not that he wanted to be a senator," he told the senator's children, "but your dad never quit anything."
The vice president joked about hustling to catch a train back to Delaware when he was a senator.
"Don't hurry, we're holding the train for Lautenberg," he said the conductor told him.
"They never held the train for me," Biden told the crowd in feigned outrage.
In the final moments before the service started, N.J. Reps. Bill Pascrell, Frank Pallone and Rush paid their respects to the Lautenberg children. Holt and Pallone are potential candidates to run in the special election called to complete Lautenberg's term.
Bonnie Lautenberg slid in next to Clinton, hugged her and spoke to her briefly.
Other services were scheduled to be held in New Jersey in the afternoon. An honor guard will lead Lautenberg's casket through the train station named after him before loading it on a special Amtrak train.
His body will lie in state in the U.S. Capitol Thursday. Burial will follow Friday at Arlington National Cemetery.
Megyn Kelly: Santa Claus and Jesus are both white men
Video of Victoria’s Secret models trying to 'twerk' hits Instagram