He says comparisons with Jermain Defoe, who went the other way when Bobby arrived in January, are futile, and explains:
"They are different types of players; I am hoping Bobby will prove himself a hero here but in a different way from Jermain.
"There are not many Jermain Defoes about anywhere because if you give it to the wee fellow he will score goals.
"Bobby is a different kind of player, probably a more intelligent footballer as such, so he has got a heck of a lot of pluses as well.
"He is his own man and he is not here to replace Jermain Defoe - and he has proved that."
Bobby scored on his home debut against Cardiff, but, self-critical that he is, was not too happy with his overall performance.
That a player who scores the winning goal in front of his own fans can still admit to being dissatisfied is a measure of the high standards Bobby sets for himself - and that Alan Pardew also demands.
"I was disappointed in Bobby in the first half," says Alan, "but in the second half when he had that clear chance I was pleased he kept his cool - because a lot of players would have snatched at that opportunity."
Peter admits that there were worries, with the Cardiff game being so tight, that the game might slip away, and adds:
"There was a bit of concern because we hit the woodwork but it turned out to be a perfect day."
Peter admits that, although Gabbidon could have gone off for a foul on Bobby, Tomas Repka could also have been shown the red card for his spat with the referee.
"We were fortunate that Tomas wasn't sent off so we got to be fair and it evened itself out," he says.
"We were disappointed with Tomas and we told him in no uncertain terms that it won't be accepted because he is too important to us."
Peter is also full of praise for Tomas' fellow centre half Christian Dailly, who played with 14 stitches in his forehead, and adds:
"He did fantastically and that is the spirit you have got to have in the team; that is something we have in abundance - everyone wants to play and is keen to do well.
"If we can match that with the quality we have we can go places; we need to put a consistent run together."
On to Burnley, then, and Peter's assessment of that.
"We were frustrated, not because we didn't do things well, because there were periods when we were very good, especially in the first half," he opines.
"In the second half we sort of stepped off the gas a little bit and it was disappointing because we were missing that little bit of fire and drive.
"We thought we could quicken the tempo later in the game and we thought the game was there to be won.
"But fair play to them, they kept battling away and if you don't put the ball in the net with the chances we had early doors, it can work against you, and they got the goal.
"Although we were disappointed with some of the aspects of the play at times in the first half we looked phenomenal.
"One thing we have to mention is that there was no lack of effort; sometimes it is a lack of the quality of what we are doing, not the quantity of it, and that is what we have to eradicate.
"Sometimes we do extra work doing nothing and once we get them working as a team - it is not about individuals - that is how we are going to win the championship.
"You have to do it week in, week out, day in, day out in your training.
"The boys are buying into that - and they came in at half time disappointed and at full time disappointed.
"That is a plus because that means they know we have to turn these draws into victories."
Peter feels progress is being made, though, and adds:
"There is a lot more to come and you always pick things that have got to improve even when you play ever so well.
"Everybody does that when they are losing, the most important thing is to do that when you are winning.
"People keep saying to me this game is important or that game is important but the first game of the season is important and the last game of the season is - and everything in between.
"All the more so when you are a big club when you have to win every game - we have got the players capable of doing that home and away and we have to do that on the pitch.
"We didn't take our chances at Burnley, and maybe the legs went a little bit late in the game; we became second to things and we have got to be better than that if we want to win at places like that.
"We could have lost that game - although we are disappointed we didn't win it."
Peter was delighted with the support - over 1,500 - at Turf Moor, and adds:
"People forget that - because you are a big club, they expect it.
"I think it is phenomenal; they went all that way and then had to travel back to go to work the next day.
"We cannot thank them enough; I am not just saying that because I want them on our side.
"I think that is what frustrates the players all the more when we don't win, the fact that the support is so good.
"But we have two home games coming up now and that support will have a massive influence on how we play, and a massive influence on the opposition as well.
"Hopefully we can turn it into a fortress at Upton Park because we are certainly getting the backing away from home, that is for sure.
"We have got to look to win every game from now to the end of the season, home or away; that is because of the quality of players we have got.
"Other teams are quite comfortable going away and getting a point but victories are our Holy Grail to get to the Premiership - and there will be no stone unturned.
"There is no faulting the effort or commitment - it is just the way it is channelled at times."