Four of West Ham's eight wins this season have come by that margin, the latest being over Wolves of course, and Peter was very happy with that.
"Hand on heart I genuinely believed we deserved to win the game but it was a case of where the goal was going to come from," he says.
"Paul Ince had a great chance when he volleyed over the bar and they did well as a team but we showed a great work ethic.
"After we got the goal we saw Wolves off quite comfortably - which was great, because people say we don't see teams off.
"I always think you should be able to win 1-0 anyway - back fours and goalkeepers are always desperate for a clean sheet.
"You might end up with 20-odd of them a season if you are going to be successful; if you are not conceding any goals you are guaranteed to be getting at least a point.
"If we could win games 1-0 to the end of the campaign I would be delighted because look at West Brom last season, and the number of wins they got by that score to win promotion.
"That was fantastic on their part because it meant they were able to defend correctly."
It was Teddy Sheringham, who also gave West Ham a 1-0 win in the second game of the season, who supplied the match winner after coming on as a substitute, and Peter adds:
"People talk about him being 38 years of age but he has also looked after himself very well and he always has that little bit of quality.
"The most important thing is that he knows himself what is right.
"We contemplated having him on the bench at Derby and if we had won at Forest he probably would have been.
"It is hard, not just for guys of 38, but for guys of 24 with the intensity and the pressure to play well every time.
"When you are constantly involved, as some of our players away on international duty are, the mental side plays a part as well.
"Teddy was honest enough to say that he felt tired but he still produced that moment of quality that he is capable of doing.
"There was a little bit of luck as well because we had made substitutions at half time and then Bobby had a bit of cramp so Teddy came on in that period and got the winner, which we were delighted about."
Peter feels the fact that Teddy could start the game on the bench exemplifies the squad mentality that exists now at the club and he says:
"If you look at the bench now it is an important part of it - they become vital to you and those not playing have been first class to a man."