The talismanic presence at Stamford Bridge had become the go-to man in west London.
Hazard often delivered and established a reputation as one of the finest players on the planet across his seven years with Chelsea.
He has now moved on, making a €100 million (£88m/$112m) switch to Madrid, and finding someone to step into his boots will not be easy – especially with a transfer ban hanging over the Blues.
Schwarzer, though, believes that those who have been operating in the shadows will now step into the spotlight, with another top-four challenge to be expected in the 2019-20 campaign.
The former Chelsea goalkeeper told talkSPORT: “It goes without saying how important Eden Hazard has been for the team over the last couple of years.
“But I just know that sometimes a player of that magnitude, a player of that importance, a player who needs to be on the ball so often, can sometimes be such a focal point that it takes responsibility away from other players.
“What’s going to happen now is there are other players in that squad who have to step up and start delivering more consistent performances.
“There are guys at Chelsea who have been hot and cold for a number of seasons, and now they have an opportunity [to prove themselves].
“They’ve lost one of the best players in the world and it’s a big loss, no doubt about it whatsoever.
“However, Chelsea have still got a very strong squad and then you take into consideration the amount of players they have out on loan.
“Frank [Lampard] is in a position, if he were to be the next manager, to say, ‘right, what’s going to work, how are we going to slot this in, how are we going to mix and match for the next 12 months?’
“I still believe Chelsea will be looking for a top-four finish.
“They are more than capable with the quality of players they have in their squad, it’s just finding the right mix.”
Chelsea already have a deal tied up for United States international Christian Pulisic, with that transfer agreed back in January.
There have been calls for the Blues to avoid putting too much pressure on the 20-year-old playmaker, but his arrival will help to counter the absence of Hazard and brings another proven creative influence onto the club’s books.