The elections saw the Conservatives get battered nationally, losing more than 1,000 seats while Labour gained more than 500 and the Lib Dems picked up over 400.
But it was a different story in Mr Street's West Midlands Combined Authority (WMCA) area, where the Tories broke even on the six councils that held elections.
The Mayor said the region's results showed people were willing to back "high-performing" Tory councils – and that the same thing could happen on a national level.
Mr Street told the Express & Star: "Across the entire West Midlands Combined Authority we lost no seats, which got to be good in a year when the party went backwards nationally.
"What we have seen is that where we have got high performing Conservative local councils, such as Walsall, Dudley and Solihull, electors have said, 'actually this is a local election and we are going to support them'.
"So the message is really clear, whether it be nationally or locally, we have got to deliver."
Asked if he had faith in the Prime Minister to sort out the party's problems nationally and deliver on policy, he said: "Yes, I do – and more so after the elections than before. The difference between us and the opposition was actually less that what many people had predicted.
"We have seen from the local elections that the electorate will reward competent delivery. It is the same nationally and there is time to achieve that before the next general election."
The local elections followed a torrid period for the Tories at the tail end of 2022, with the party having three leaders in a matter of months in the wake of the Partygate scandal.
In the WMCA areas the Tories picked up two seats in each of Sandwell and Solihull. They finished level in Dudley, Walsall and Coventry and lost three seats in Wolverhampton. There were no elections in Birmingham.
The projected national share of the vote put Labour on 35 per cent, ahead of the Tories on 26 per cent and the Lib Dems on 20 per cent.
The picture would likely result in a hung parliament should it be repeated at the next general election, which is expected to take place next year.