The Demons are in a 0-5 hole after Bombers captain Zach Merrett dominated in his side's 15.6 (96) to 8.9 (57) victory at Adelaide Oval on Saturday night.
Essendon ruck Nick Bryan will be sent for scans after suffering a suspected season-ending knee injury.
But Merrett's game-high 38 disposals and the feats of Dylan Shiel (30 touches) and Jye Menzie (four goals) were instrumental in Essendon squaring their win-loss ledger at 2-2.
Goodwin's Demons, though, sink to 17th, above only West Coast, with an alarming lack of scoring potency - averaging about 60 points a game.
"We've had a lot of challenges through my time at the footy club," Goodwin said.
"I have been pretty well serviced to see the club through that and I feel pretty well credentialled to do that.
"'We're in a challenging spot right now and we acknowledge that.
"But my focus is just doing my job to the best the ability and I believe I've got the credentials to do it."
Melbourne produced a third-term rally before a crowd of 45,039 on Saturday night. The oval's earlier game - Carlton's 71-point hammering of the Eagles - attracted 41,252.
But the damage had been done: the Demons were within six points early in the second term before Essendon kicked the next five goals for a 35-point lead in the third quarter.
Just when Melbourne appeared down and out, they suddenly - and unexpectedly - turned the tide with four consecutive goals in a 15-minute burst.
The Demons were 10 points down when busy Bomber Nic Martin goaled in the 32nd minute, giving his side a 16-point cushion at three quarter-time.
Essendon then scored five goals to one in the last term to settle the Demons' fate.
Melbourne will lament allowing Essendon to produce a telling quarter-hour in the second stanza when the Bombers kicked four consecutive goals.
The batch was book-ended by the influential Menzie, whose third goal created a 30-point break.
At that stage Melbourne, renowned in recent years for a misfiring forward line, led the inside 50 count 25-22 but had scored just 2.4.
Essendon's 7.4 to 2.5 halftime lead was soon increased to 35 points before the Demons' unheralded four-goal, 15-minute spree.
But Melbourne's best period was too brief to overpower the Bombers, who earned praise from coach Brad Scott.
"We were on for most of the game," Scott said.
"Melbourne to their credit really challenged us in that third quarter but I thought we showed pretty good character to respond to that challenge."
Essendon claimed midfield honours with Merrett, Shiel, Ben Hobbs (20, two goals), Andrew McGrath (26 possessions) and Nic Martin (28, one goal) all shining.
Demons winger Ed Langdon was a standout with 25 touches and a goal while big guns Pickett (23, two goals), Christian Petracca (27 possessions) and Clayton Oliver (24 possessions) all had impact.
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