"You have to be professional and focus on the job in hand and any time you turn up you have to prepare and do your job correctly.
"If we do that we should win the game - there is no use kidding yourself that you shouldn't.
"Southend in the last round gave as good as they got and we had a few young boys coming in for their first game, and it was a tight win.
"But if we play to our potential we will win the game; you need that little bit of luck to go your way as well, and we will give them the utmost respect.
"We have had them scouted three or four times and there is no problem about underestimating them in any shape or form because we want to go as far as we can in the competition - and we feel we still have to improve as a team.
"Every game is important to us because we want to take West Ham forward."
Peter says that the difference in the two clubs' status on Tuesday night will count for little when the whistle goes, and he adds:
"We must start right against Notts. County because on that pitch, even if someone is earning £1m a year and someone else is earning £1,000 a year it doesn't mean any difference on the football pitch.
"It means one player should have the better quality but at the end of the day you have to earn that on the pitch."
There are, of course, changes in the squad with Chris Powell not given permission to play by Charlton and Calum Davenport and Carl Fletcher cup-tied.
"Most of the changes are forced; we want to go as far as we can in the competition and we are not taking it lightly," says Peter.
Teddy Sheringham is rested and Peter explains:
"With Teddy, who is 38 years of age, he has played a heck of a lot of games - probably more than we expected him to - and he has a lot of games still to come.
"He looks after himself very well and he is a very good professional but we have to be careful; it is quality you want, not quantity.
"Maybe this is a good time to give him a rest and there are others, such as Bobby Zamora and Sergei Rebrov, waiting for an opportunity.
"Hopefully they can come in and throw their hat into the ring for a starting position."
Young strikers Moses Ashikodi and Greg Pearson are in the squad as well and Peter adds:
"There is a possibility that either one or both could be on the bench; this is an opportunity for them because we are a bit light up front.
"Who knows? if we are doing well enough you would hope to get the youngsters on, but, as was proved in the Southend game, it is difficult - they probably deserved something in the second half of the game.
"So we won't be treating the game lightly, but if we get the opportunity to blood some youngsters it would be fantastic - though we would need to be winning very convincingly for that."
Moses Ashikodi has been prolific since joining from Millwall in the summer and Peter says:
"He has a lot to learn in his game to make him a better player but if you have an eye for scoring goals that is something you can't teach, it is just a natural instinct.
"The boy seems to have that but he does have to mature as a player."
Steve Lomas and Bobby Zamora are likely to figure and Peter says:
"It will be fantastic to have them back; people talk about big squads but you have to have quality in that and hopefully they can stay injury free now.
"I have had it all my career that you always seem to play better when there is somebody challenging you - the big players respond to that.
"We never push anyone out of the side and do away with them because we always feel that they have something to offer the team - a player has to be ready to grab the opportunity when he comes in, and when he is in he has to play well to stay in the side."
Meanwhile, Peter has revised his opinion of the performance against Ipswich on Saturday and reveals:
"Me and Alan sat down and watched the game over the weekend and we feel that, apart from a 15-minute period at the start of the second half when Ipswich dominated because we were giving possession away cheaply, we were excellent.
"When we looked at the video, all in all we played better than we actually had thought we did - so we were probably more critical of the players than they deserved.
"But we have been in that scenario at Upton Park often enough when we have so much possession and chances and we don't seem to kill teams.
"If we had scored the second, whether with the penalty kick or with some of the other chances we had, we would have won the game quite comfortably.
"I am sure of that because of the way we were playing; everyone was going about their job correctly - we were in their faces, making it very difficult for them to get started.
"Maybe they put so much effort into the first half, dominating it for so long, that a bit of tiredness crept in for about 15 minutes after the break.
"Then, when we got going again, we played a hell of a lot of good stuff.
"There aren't going to be many games where we walk over the top of anybody but we have to add that ruthless streak in both boxes, defending well and taking your chances.
"We have played less well and won - and the players would admit that as well.
"When me and Alan finished watching the video we were scratching our heads a little bit because we obviously didn't realise we had played so well in the second half.
"I turned to Alan after looking at it and said 'there was a heck of a lot of good stuff after the break'.
"Hopefully we are getting to go in the right direction slowly but surely, though sometimes when you think everything is going well you get a kick in the backside."