Hazard starred during seven campaigns at Stamford Bridge, but made a close-season move to Real Madrid for a reported €100million (£92.7m).
The Belgium international was directly involved in 31 Premier League goals (16 goals and 15 assists) during the 2018-19 season and his departure leaves a huge hole for Chelsea to fill.
Lampard said Hazard – who won two Premier League titles and two Europa League crowns with Chelsea – could not be replaced by just one player.
"I was a huge fan of Eden Hazard as a Chelsea fan, I played with him," he told a news conference ahead of his side's UEFA Super Cup clash against Liverpool on Wednesday.
"For me, clearly one of the best players in world football and last season, but not just last season, over his time at Chelsea he was the most productive player in the team generally, in terms of assists and goals and a leader.
"You cannot replace him individually, I think it's pretty much impossible because of the high, high level he is at now in his career.
"But the good news and the positive news for us and we must stay calm and be patient with this [is] we have a group of players, some younger players, some experienced players, that now have the opportunity to show that collectively and individually they can step up because yes, you are missing a huge amount of assists and goals, that's clear.
"The answer is as a team, we have to find a way to carry on because a football club like Chelsea will always carry on. Eden Hazard, John Terry, Didier Drogba, players improve on and it's down to the next players, the next manager. That's our big challenge now, to say good luck to Eden Hazard and to carry on as Chelsea."
Lampard's first competitive game in charge was a miserable one, with Chelsea humbled 4-0 by Manchester United at Old Trafford on Sunday.
Still, the former Derby County boss believes in his team ahead of their meeting with the European champions in Istanbul.
"I am optimistic because I believe in the players and I believe in the fact we are here in the final because we deserve to be," Lampard said.
"That is the achievement of the players and the club last season, not myself, but I am proud to be here managing the team.
"I understand the quality of Liverpool, the team that deservedly won the Champions League. They have an outstanding manager [Jurgen Klopp] and group of players and we know it is going to be a big test, but I believe in my players and if we play to our maximum we can win the match."