The former Labour deputy leader said Yvonne Davies, who has led Sandwell Council for the past eight months, lacked the skill and "humility" to guide the authority away from its scandal-riddled past.
He accused her of letting down residents and said her "arrogance" had foretold Labour's disastrous general election performance.
“It’s not for me to decide as I am completely out of Sandwell politics, but if I was still there I would definitely be asking for her resignation,” he said.
He also slammed Labour's West Midlands regional office, describing it as "an outpost of the London headquarters" which needed "root and branch reform" under Jeremy Corbyn's successor.
Mr Watson was the MP for West Bromwich East for 19 years before quitting frontline politics ahead of the election.
In an interview with the Express & Star, he argued that there was a direct link between Labour's slump at the polls and the failings of the party's West Midlands office.
And he said the running of Sandwell Council – which had three leaders over a five month period last year – was an example of how interference from national figures had hurt the party locally.
'Never got over the scandal'
He said the council had undergone "a rocky few years" since the publication of the Wragge report, which detailed allegations of wrongdoing against ex-councillor Mahboob Hussain centring around land sales.
"They have never really got over the scandal, and until they resolve it I think it will be very difficult for them to move on," he said.
"I was extremely disappointed with the current leader [Ms Davies] when she refused to meet the residents of Friar Park, who were concerned about the concrete sleeper factory being built in their back gardens.
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"It showed an arrogance that perhaps foretold the general election result in December.
"I would imagine that the members who are running Sandwell Labour Party are having a very deep think about how they can show a more humble response of leadership."
The council has this week named its former executive director of adult social care health and wellbeing David Stevens as its new executive. Mr Stevens had temporarily been in the role since Jan Britton stood down five months ago.
Labour lost five Black Country seats in the election – including Mr Watson's old one, Dudley North, West Bromwich West and two in Wolverhampton.
Mr Watson said that "poor organisation" from Labour's regional office had contributed to the defeat, with candidate selections increasingly organised by national officials.
"The results in the West Midlands were clearly, worse than anywhere else in the country and I'm sure Labour's review will want to look closely at the operation of the regional office to see whether improvements can be made next time round," he said.
"When I was elected in 2001, the regional team that ran the West Midlands office were considered the very best in the country. Tony Blair's success was winning back seats here. That was helped by some very accomplished political organisers.
"We have clearly lost a lot of that expertise in recent years, so there's a lot of personnel issues that need to be looked at.
"The West Midlands has always been fiercely independent, and if you have a regional office that is basically an outpost of the London headquarters it is not going to do anyone any good."
He added that candidates being parachuted in from London without local members having a say, such as Ibrahim Dogus in Mr Watson's old seat, had been a major error.
"Ibrahim Dogus is a very nice man, but it is a very big ask to expect a West Bromwich voter to vote for someone they have never heard of, who is the current Mayor of Lambeth," he said.
"I'd like to think that had Labour HQ allowed a local councillor on the list, then the outcome might have been different. The role of a regional office is to be very clear about how constituencies can be won.
"That's not just down to message, or fundraising, it's about the type and calibre of candidate they put forward.
"I'm sure the new Labour leader will want a root and branch reform of the West Midlands office."
Ms Davies said she did not meet residents regarding the sleeper factory as she did not wish to give them "false hope", saying Sandwell Council had no influence over the proposals.
Responding to Mr Watson's call for her to resign, she said: "Mr Watson is a complete irrelevance in my life.
"I have a big piece of work to do in Sandwell. If I took notice of all the disgruntled people who had a go at me I would never get any work done."
A West Midlands Labour spokesperson said: "The process for selecting candidates had to be accelerated because of a snap election being called three years ahead of schedule.
"This was done in the West Midlands in line with the same procedures laid down by the NEC for all of the nations and regions.
"We thank Tom Watson for his service to the people of West Bromwich East and to the Labour Party and wish him well in his new career."