The 18-year-old was rewarded for a promising Carling Cup display against Everton last month with a full Premier League debut at Liverpool on September 26.
It proved a baptism of fire as Fernando Torres grabbed a hat-trick in Liverpool's 6-1 win and, despite earning praise for his showing, Cooper was left out against Wigan last weekend.
"Liam Cooper will play Premier League football, I guarantee that," said Brown. "The lad has got a future in the game and it is at this level, I have no doubt about that.
"But you just don't throw your kids in every week unless they are exceptionally talented or it is above and beyond the call of duty."