Cook remains under mounting pressure after the drawn first Investec Test against India at Nottingham, where his England team extended their sequence without a win to nine matches stretching back 11 months.
He could also muster only five runs, taking his annual tally to a meagre 97 in seven attempts, before he was freakishly bowled round his legs off the underside of his thigh pad.
There is precious little time to regroup before the second Test at Lord’s on Thursday.
“It is a tough time when you are not getting runs,” Moores said. “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,” added Moores.
“He will be very keen to put his mark on Lord’s.”
Yorkshire’s Joe Root is England’s highest-ranked batsman in the ICC Test rankings at 16 following his unbeaten 154 in the draw against India at Trent Bridge.
South Africa’s AB de Villiers holds the No 1 spot and Yorkshire batsman Gary Ballance’s 71 saw him move up 13 places to 70th.
Sri Lanka batsman Mahela Jayawardene, 37, is to retire from Test cricket.
Jayawardene has made 11,493 runs in 145 Tests at an average of above 50.