The captain, who has made 25 centuries during his 102-Test career, has scored just 97 runs in his last seven innings for the international side.
Moores told Sky Sports News: "It is a tough time when you are not getting runs. But Alastair is a tough player, as he has shown throughout his career.
"It is a five-match series, and in a five-match series I expect Alastair to come through strongly, because he is a top-flight player. He has to stay strong.
"He has been through this situation before, and that is what makes great Test players, they can ride through it and come back strong, He will be very keen to put his mark on Lord's."
England's second Test against India gets underway on Thursday.