Moyes masterminded the dramatic fourth-round replay victory at Stamford Bridge, which saw the Toffees become the first club to beat the Blues in the cup for almost three years.
There were echoes of Everton's 2009 Merseyside derby win at the same stage of the competition, after which they went on to reach the final.
"To be through in the cup gives you a great boost," he said.
"If you put out the team who are the holders and the champions, you've got to think that you've got a good chance."
Source: PA
Source: PA