Research shows that, if the UK were to remain in the European Union, UK regions would have received 13 billion Euros over the seven years between 2021 and 2027 - 22 per cent more funding than the current funding programme, which runs until 2020.
Mayor Jarvis, who is also MP for Barnsley Central, said South Yorkshire would have been an even greater increase in funding, from 117 Euros per head to more than 500 Euros per head.
The mayor led a debate in Westminster Hall on Tuesday urging Government through the new post-Brexit UK Shared Prosperity Fund to tackle the gap between the richest and poorest regions.
South Yorkshire MPs Clive Betts, Paul Blomfield, John Healey and Caroline Flint also took part in the debate.
Mayor Jarvis said: “(This is) an opportunity for us to look at this issue through the eyes of our communities rather than through the prism of party politics.
"I am in a unique position as Mayor of the Sheffield City Region and also MP for Barnsley Central. I have seen first-hand what local areas can do when they come together to drive economic growth. But I’ve also seen how limited and constrained they are by the powers and resources available to them.
“Both European and Government funding often comes with limitations that inhibit creative thinking, making it virtually impossible to deliver the significant structural changes that we need.
"The UK Shared Prosperity Fund presents an opportunity to press the reset button and think about how we do things differently. This must be the start of our economic transformation, not the end.”
In the debate, Mayor Jarvis said the fund should be ‘no less in real terms’ than both the EU and Local Growth Funding streams which are set to end adding there must be a ‘guarantee by Government’ that regions will not be worse off in terms of funding beyond 2021 because of Brexit.
The mayor went onto say there must be an ‘open and transparent process’ in place that ‘strikes a balance’ between areas of need and supporting those economies with the greatest potential to grow.
Jarvis made the point of the UK of having one of the most centralised finance systems adding more should be done to devolve more money to councils and mayoral authorities.
He said: “This country has one the most centralised systems of public finance and political control amongst all the Organisation for Economic Co-operation and Development countries.
“The Guardian reported controls only 1.6 per cent of gross domestic product. It’s six per cent in France, 11 per cent in Germany and 16 per cent in Sweden – yet it’s local government that delivers around a quarter of public services.
“The inevitable consequence is decisions, however well-meaning they may be, do not always reflect the needs or the opportunities of local areas.”