Hazard left the club after seven seasons this summer to join Real Madrid, but the Blues have been prevented from bringing in new players by a transfer ban.
Per Goal's Dejan Kalinic, Lampard said his former team-mate is among the best in the world and was a leader in the Chelsea dressing room, as well as their biggest source of goals and assists.
"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 spoke ahead of Wednesday's UEFA Super Cup final, in which his side will take on Liverpool.
Hazard played a key role in Chelsea qualifying for the match by scoring twice in the UEFA Europa League final last season:
The Belgian's final season at Stamford Bridge saw him return 21 goals in all competitions—his best tally with Chelsea in a single campaign—as well as 17 assists.
He enjoyed a great deal of success during his time with the Blues, per Soccer Laduma's Dave Kappel:
Hazard's departure would never have been easily dealt with, but it did come at a particularly inopportune time for the club, who could not register new players this summer and can't in January, either.
Chelsea were able to bring in Christian Pulisic, though, as he was signed last January and loaned back to Borussia Dortmund for the second half of the 2018-19 campaign.
The American is an exciting prospect, but he's only 20 years old, so he cannot be expected to replace Hazard's match-winning contributions alone.
As Lampard noted, particularly until Chelsea can dip back into the transfer market, it will take a collective effort from his squad to compensate for the winger's departure.
The likes of Olivier Giroud, Willian, Ross Barkley and Pedro can also be match-winners on their day.
While individually they're not as consistently decisive as Hazard, between them they can give the Blues plenty of potency in the final third if they can each have strong campaigns.
If Pulisic and other younger players such as Tammy Abraham and Mason Mount can also do their part, that could keep the Blues competitive before they can recruit again.