The Conservative Mayor said it was "very disappointing" that the West Midlands Combined Authority area will be placed under the highest level of Covid restrictions when the national lockdown ends on December 2.
He has laid out a series of demands for financial support from the Government, and also urged Ministers to provide evidence for closing down the region's hospitality sector.
The move to Tier 3 means all hospitality venues must stay closed except for deliveries and takeaway, a move the Campaign for Real Ale (CAMRA) said was "especially devastating" in the run-up the Christmas.
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Mr Street said that while the strictest measures were understandable given the high rates of infection in the West Midlands, the Government needed to publish "de-escalation thresholds" so regional leaders would know when areas could drop down into less restrictive tiers.
He called for further financial support, saying the existing £3,000 monthly grant scheme was "insufficient" for medium-sized and larger businesses that were forced to close, particularly those in the hospitality sector.
He also requested a targeted package for the conference and exhibition sector, and a mirroring of the self-employment scheme for businesses currently "frozen out" of financial support.
Mr Street said: "The Government also needs to provide clear epidemiological evidence as to why the hospitality sector is forced to close in Tier 3."
The mayor said he hoped the region could move out of Tier 3 before Christmas.
"Whilst people might disagree with this non-negotiable decision, what is now critical is to ensure the region moves out as safely and quickly as possible," he said.
"Given the trajectory our rate of infection is on, I am hopeful it won't be long before we see a shift to Tier 2."
Mr Street has also called for further support so local authorities can boost testing regimes and vaccination preparations.
His concerns were echoed by Andy Burnham, the Labour mayor of Greater Manchester.
Mr Burnham said the measures – which mean pubs and restaurants have to stay closed except for deliveries and takeaways – would cause “real hardship”.
The mayor, who clashed with ministers over the levels of support available when the region was first put into Tier 3 before the current lockdown, said it was “completely wrong” that there was no additional funding.
“The new Tier 3 will hit the hospitality sector extremely hard. While there are grants for businesses forced to close, there is no extra support for business which supply them like security, catering and cleaning,” he said in a statement.
“This will cause real hardship for people whose jobs will be affected and risk the loss of many businesses.”