The Blues manager tasted defeat in his first Premier League game as a coach on Sunday evening following a chastening 4-0 loss to Manchester United at Old Trafford.
Although Chelsea FC hit the woodwork twice in the first half, the Red Devils eased to a comfortable victory courtesy of goals from Marcus Rashford, Anthony Martial and Daniel James.
The west London side appointed Lampard as their new manager in the summer after Maurizio Sarri left Chelsea FC to take over the reins of Serie A champions Juventus.
Lampard was unable to recruit his own players as Chelsea FC served a transfer ban in the summer months.
The Blues sold their prized asset Eden Hazard to Real Madrid to weaken their squad ahead of the new season.
Former Chelsea FC striker Sutton is worried for Lampard given the west London side’s limited squad.
“It’s like going into an Olympic rowing final and being asked to compete in a dinghy,” Sutton told BBC Sport.
“And you’ve lost your Steve Redgrave.”
Sutton added: “Frank Lampard has one hell of a job on after the club lost their best player.
“Hazard carried them for years but he’s gone and they can’t bring players in.
“It all comes down to what the owner’s expectation is and what Lampard has been told at the start of the season. The fans being behind Lampard will only last for so long.”
Chelsea FC finished in third place and won the Europa League in what turned out to be a positive season for Sarri despite on and off field controversies.
The Blues brought in Christian Pulisic and Mateo Kovacic in permanent deals in the summer after agreeing to transfer with the two midfielders earlier this year.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news