Barnwell wants managers and referees to hold more meetings to try to develop a greater understanding of the demands of each other's profession.
Among the topics he wants debated is a possible cooling-off period for managers at the end of the game before they confront match officials or the media. His comments follow an outburst to the press by the Coventry manager, Gordon Strachan, within five minutes of the end of Saturday's 2-2 draw with Arsenal, in which he claimed referees were giving his side "nothing".
Barnwell said: "What we don't want to do is inflame this situation and people are trying to whip up an `us and them' situation between managers and referees which is not the case.
"If you aren't careful you can end up with a very entrenched position of `them and us' and it's not that. What the aim of everyone should be is for the improvement of the game."
Another manager wanting more clarification from officials is Leeds' George Graham who yesterday called on the Football Association and the Referees' Association to issue uniform guidelines on the use of video evidence.
Graham was taken aback by Steve Lodge's decision to review the dismissal of the Coventry defender Paul Williams after the match against Arsenal.
Just over two weeks ago Graham had asked Mike Reed to review the sending- off of keeper Nigel Martyn at the end of his side's 4-0 FA Cup third-round victory over Oxford - in both instances a player was prevented from scoring.
Reed declined, with Graham told he would have to write to the FA enclosing a copy of the video, although Leeds were promptly informed that the only grounds for appeal were for mistaken identity or violent conduct.
Martyn served a one-match suspension while Williams could have avoided a ban if Lodge had changed his mind.
Graham said: "I wish the FA and the Referees' Association would get their act together so we know the correct procedure for sending-off appeals.
The FA and the Referees' Association, however, both agree the referee should have the choice over whether to review a video if he feels a decision could be overturned.
An FA spokesman, Steve Double, said, however: "If the referee chooses not to review a particular incident then the club lodges an appeal and we will see if there are reasonable grounds and whether we should refer it back to the referee."