The pundit has lauded the West Ham striker and manager.
West Ham came back from 2-0 down to beat the Toffees 3-2 and Bilic's introductions of Carroll and Diafra Sakho made a big difference.
Keown told MOTD on Saturday night: "The manager makes a change. Carroll came on and then Sakho. And Carroll just creates mayhem.
"Bilic is thinking to himself - ‘how good am I for making those changes!?’"
Bilic has certainly brought some managerial class to the Hammers.
While West Ham's players, owners and fans have all played big parts in their season so far, Bilic has been crucial to their fortunes.
His approach appears to be to keep things as simple as possible. The Croat wants to keep the players happy, not overcomplicate things tactically and make changes during games when they need to be made.
After West Ham's 1-0 loss at Southampton, supporters were disappointed with the east London side. But look at them now - a Champions Place is firmly within sight.