The Hammers enter the third round stage facing Everton at Upton Park, and Peter says: "The first team are finding it difficult at the moment so hopefully we can make the club a little bit happier with a result.
"It is the mainstay of youth football, recognised as the best tournament, and we have normally done fairly well in it so hopefully we can continue."
Of the opposition, he says: "They are decent by all reports - very strong, quite physical and dogged so I think it is going to be a tough game.
"They won't be able to defend and get a draw because it is a one-off, and the result has got to be settled tonight, so hopefully they might come out and play a little bit and help make it a very decent game."
Some of Peter's charges will be involved on the night, and he adds: "We are going to be quite young as a youth team but I don't think that will make any difference to our performance and hopefully we can do all right.
"From the starting line up I have got about five of mine in it, so full marks to the them for getting through into the 18s and 19s - that is a decent sign, and in fact three of the back four are first years."
Peter has reminded them they can do their quest for stardom no harm at all in front of the club's decision makers and says: "Me and Tony Carr said to them this morning that everyone will be there from the directors to the management of the first team, it is at Upton Park, and it should be a decent crowd.
"The boys who are playing will do themselves a world of good with a decent performance, with the right people watching them.
"It is entirely up to them; hopefully some of the players with a reputation don't freeze on the evening and one or two of the others do well.
"And I expect all the academy boys will be there; they will come and learn something, look at it and say 'hopefully we can go as far as that and be part and parcel of it in a few years'."
Peter's Under-17 side lost 2-0 at the weekend against Aston Villa.
"We had five schoolboys out against a very strong side who only got their second goal with the last kick of the match," he says.
Team: G.Sealey, Wright, Lumsden, Fletcher, McLenahan, Collington, Carrick, Tucker (Bouton), Cole (Lee), Morris, Pearson. Subs unused: Bluett, Bunce.