Lampard’s side were gifted their goals by an error-filled display from United goalkeeper David De Gea, but Chelsea were deserved winners as they dominated the semi-final from start to finish.
Olivier Giroud opened the scoring late in the first half and Mason Mount got the second after the interval at Wembley.
Harry Maguire’s own goal killed off United before Bruno Fernandes’ late penalty.
After some shaky performances in recent weeks, including a 3-0 hammering at Sheffield United, Lampard was impressed with the spirited way his players out-classed in-form United at Wembley.
“I can’t ask for any more from my players than that. The work ethic and the level of performance. We were on top and when they changed their system we were even better,” Lampard told the BBC.
Chelsea’s victory moved Lampard a step closer to silverware in his first season in charge of the club where he earned legendary status as a player.
Before their FA Cup final date with London rivals Arsenal on August 1, Chelsea have to focus on qualifying for the Champions League via a top four finish in the Premier League.
They sit third — one point above Leicester and United — with games against Liverpool and Wolves to finish the league season.
“We have finals ahead. Two in the league and then Arsenal,” Lampard said.
“We want to win things, and at the start of the season we wanted to be up there challenging for the top four.
“A lot of people were tipping against us, but quietly I was always hoping.
“I don’t want to put everything on these three games defining everything we’ve done and the progress we’ve made, but of course we want top four, we want trophies and we’re at the business end, so let’s see.”