The 20-year-old showed his power, pace and awareness to outshine Arsenal's Mikel Arteta and Mesut Ozil on Sunday with a performance of real maturity.
"I've never seen a young English player with his sort of mentality," said Martinez.
"I can see some (Michael) Ballack in him and some Gazza (Paul Gascoigne). It's fine for us to make comparisons but he is Ross Barkley. He has great balance, is good with both feet and is developing an incredible awareness.
"You can compare him against any of the best young Brazilians, Dutch or even Spanish."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball