Steve Cotterill and Sean O’Driscoll both refused to reveal the reason for Saturday’s remarkable touchline feud.
The former Bournemouth team-mates had two lengthy confrontations during the Keepmoat Stadium fixture.
The pair initially clashed when Cotterill kicked the ball into his dugout when it was a Pompey throw.
After home substitute Byron Webster had words with the Blues boss over perceived time wasting, O’Driscoll then waded in, prompting a heated discussion between the managers.
At the final whistle, the Doncaster boss approached Cotterill to shake his hand and, after doing so, the pair had another set-to.
Pompey ran out winners 2-0 to make it a miserable day for O’Driscoll.
But Cotterill afterwards declined to lift the lid on what went on between the sparring duo.
He said: ‘From my perspective, I really would rather not speak about it.
‘I have had my say to him, I don’t need to say any more and I don’t need to make it public, either.
‘I just don’t think it’s anything to do with Saturday afternoon. Let’s just leave it at that.
‘What has gone on there, what was said down there is between me and Sean, that’s it.
‘I have known Sean a long time and he has known me for a long time, let’s just leave it at that.’
O’Driscoll was also determined not to explain what went on between the pair.
The softly-spoken boss spent two years with Cotterill as players at Bournemouth.
The pair have kept in touch since but he chose to avoid revealing what went on during the match.
O’Driscoll added: ‘That is between me and Steve Cotterill.
‘It was like two kids in a playground. I know Steve really well.
‘I’ve got no bug bears, it’s too short a career in football to hold grudges.
‘At the end of the game we have lost so anything I do looks like sour grapes.’
Meanwhile, Cotterill blasted the late dismissal of Jonathan Hogg for two bookable offences.
A late handball saw referee Andy Haines give the on-loan midfielder his marching orders and he will now miss next week’s visit of Barnsley.
Cotterill said: ‘I can’t believe Jonathan Hogg was sent off. I cannot believe that.
‘But I thought we got absolutely nothing. We couldn’t even get a throw-in that was ours.
‘If that’s not ball-to-hand, I don’t know what is.
‘You can’t even appeal it because it’s two bookings, that’s the worst thing about it.
‘Ridiculous, absolutely ridiculous.’