The former Swansea City midfielder has yet to make an impact at Bramall Lane following his summer move north but Speed is fully aware that it takes time to settle in at a new club.
"It took me a long while to adjust when I moved to Newcastle and Everton so we have to give him time to do that here," said Speed ahead of his first home match officially in charge of the Blades.
"Our fans need to be patient – although I'm certain he won't be fazed by anything."
Britton rejected interest from a Premier League club to join the Blades and insists that he has no regrets despite the club's current position at the bottom of the Championship table.
The Blades, meanwhile, have announced a tie-up with the football authorities in Syria – the latest in a string of global partnerships.