And Prior knows England cannot afford to be distracted by reported problems in the opposition ranks.
He was at pains to make those points, even as the contents of sacked former Australia coach Mickey Arthur's legal documents - he is suing Cricket Australia over his dismissal - were telling the world of apparent personality clashes in the dressing-room he vacated last month.
England believe it is a blind alley to be sidetracked by other people's issues when they still have plenty of their own to address, two days after going 1-0 up in Nottingham and two before they must try to consolidate that lead in the second Investec Test at Lord's.
"Quite honestly, we have our own things to worry about - making sure our own team is right and we're playing the best we can play," said Prior.
"We know we haven't played to the best of our abilities in that last Test match and that's what we want to do.
"The minute you take your focus off that is when you come undone."
England held on in the tensest of finishes for a 14-run win on Sunday, when Ian Bell's second-innings century and James Anderson's 10-wicket match haul were the major factors in their success.
Prior added: "I think we can improve in a number of areas ... and that's not a negative thing at all.
"To play not as well as you can and still win the Test match shows a huge amount. If we can really hit our straps well with bat and ball, we will be a pretty tough team to beat."
Among those who took part in the first Test, Steven Finn is alone in that his participation - on his home ground on Thursday - is not guaranteed, injuries aside.
Finn took two wickets in two balls in the first innings, but ended up with match figures of two for 117.
Tim Bresnan and Graham Onions therefore come under consideration to replace him in the third seamer's role.
Prior, however, expects the tall pace bowler to be in the reckoning again.
"Steven Finn is a fantastic talent and a fantastic bowler for us, and has put in some winning performances for this England cricket team," said the Sussex man.
"Everyone can have a bad day or a bad game - that happens - but we'd expect Finny to bounce back stronger than ever and to come steaming in bowling with good speed and good pace - like he does and like we see in training and nets and everything else.
"We know how good Steve is and we know he'll be coming back fine."
Prior has been short of runs himself so far this Test summer, but is confident he has plenty more in him - especially after his most recent contribution.
"I probably couldn't get a better 31 than I did the other day," he said.
"I felt in great rhythm, felt in good form.
"You get a feeling it's going to be your day and I felt it was going to be my day.
"To toe-end two deliveries straight to blokes is slightly unfortunate, but that's the way the game goes."
He was also able to scotch any lingering concerns about his fitness.
Reports on Monday suggested his absence from England's annual golf day was because of his ongoing Achilles trouble and meant he might not make it to Lord's.
But he said: "My Achilles feels better than it has done for a long time.
"The reason I didn't play golf is simply because, with back-to-back Ashes Tests and only one day off, I wanted to put my feet up and rest.
"I didn't want to risk flaring it up and doing something stupid. Can you imagine what you guys would have say if I injured myself playing golf on my one day off?"
Anderson was also missing on the greens and fairways, as he paces himself for more important assignments after his marathon efforts with the ball in Nottingham.
"I don't think there are many players who are not trying to manage something," added Prior.
"Jimmy didn't play yesterday [Monday] either, simply because of the workload he is under.
"His best chance of getting fresh for Thursday was having a day off his feet."