The Remainer said it was “quite right” other areas of the UK looked at Stoke and how Brexit could work for the city.
Stoke is hoping to attract high paying employers back to the city, which has suffered many industry closures after a rich history in trades including pottery and mining.
Mr Snell, who previously tweeted a four line poem describing Brexit as s***, said Stoke had “forcefully” made its voice heard and it was up to local MPs and the Prime Minister to make sure the city thrived.
Gareth Snell said if Brexit can work in Stoke, it can "work anywhere"
It’s quite right that people focus on us and look at us
Speaking on BBC Radio 4’s Today programme, he said: “What we’ve got to do now is make sure Brexit works for the Potteries and that the Brexit deal that Theresa May is going to go and negotiate has a real impact and benefit here in Stoke-on-Trent.
“I think, given how forcefully Stoke made its voice heard in the referendum and given how strong that vote was for Leave, I think it is absolutely right that we can now say look, the people of Stoke have given Theresa May the mandate that she now has to go and negotiate.
“If she can make it work for Stoke-on-Trent and we as local MPs can negotiate what we need, then I think yeah, it’s quite right that people focus on us and look at us because if it can work here, it can work anywhere.”
Brexit: Results of how the UK voted Mon, March 20, 2017
Much of the North East of the United Kingdom voted to leave the European Union including Sunderland, Gateshead, Darlington, Durham, Hartlepool, Middlesbrough, Stockton, Redcar and Cleveland, North Tyneside and South Tyneside, and Northumberland
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GREAT YARMOUTH: The town of Great Yarmouth on the East Coast of England voted by 72% to leave the European Union.
Mr Snell posted a poem reading "Soft Brexit, hard Brexit/Massive pile of s***” last September.
Around 70 per cent of people in Stoke-on-Trent voted to leave the EU.
The Prime Minister will trigger Article 50 and begin Britain's historic departure from the European Union on March 29.
The move will kick-start the beginning of the two-year countdown until Brexit is complete.