Pyrotechnic flares were set off before kick-off outside the club's Brunton Park stadium and later inside the ground, with one thrown into the crowd.
At Carlisle Magistrates' Court, two males, aged 17 from the Carlisle area, were given three-year banning orders.
They were also handed three-month youth offending orders.
The 31 January fourth round tie ended with a 3-0 win for Everton.
Cumbria Police said an 18-year-old man remains on bail until 28 April in relation to alleged racist chanting at the same game.
Two teenagers have been handed banning orders after flares were set off at Carlisle United's FA Cup game with Everton.