Kean claimed Singh's comments made about himself and midfielder Morten Gamst Pedersen have disrupted preparations for the new season.
Rovers begin their quest for an instant return to the Premier League at Ipswich on Saturday, but - as has been the case far too often at Ewood Park in recent times - the build-up to an important match has been overshadowed by off-field controversy.
Speaking at an open meeting with fans last weekend, Singh stated Kean - deeply unpopular among sections of Blackburn supporters - would be dismissed from his post if he lost three consecutive games early on in the season.
The former Malaysia defender and television pundit went on to liken long-serving Norway international Pedersen to a "pensioner".
Singh apologised for his comments earlier this week but that failed to satisfy the Professional Footballers Association, who issued a statement in support of Pedersen this afternoon following talks with union representative David Dunn and members of the Rovers squad.
The statement chastised Singh's "subsequent apology which didn't seem to retract the comments, rather Mr Singh simply implied he was 'too honest for his own good"', a point of view Kean appeared to subscribe to when addressing the media shortly after it became public.
"I don't really think it was an apology," he said.
"I think there was an apology that feelings might have been hurt and people might have been rubbed up the wrong way, but I don't really see a retraction being in there.
"So, we'll just move forward. I don't really want to discuss it any longer. I'd rather focus because it's been massively disruptive this week and we just want to get on with the job in hand which is getting prepared for Ipswich.
"It's massively disruptive in a very important, if not the most important week. I think that statement shows how disappointed and unhappy the players are with it.
"Morten has been a fantastic servant. He's probably one of the true gentlemen and it's really affected him."
For his part, it seems Singh - appointed this summer to mediate between Blackburn owner Anuradha Desai and Kean - is unlikely to keep a low profile as he is slated to fulfil radio summarising duties for BCC Radio Lancashire on Saturday.
Irrespective of Singh's comments, Kean was set to begin the forthcoming campaign under significant scrutiny, but he points to summer acquisitions such as Danny Murphy, Nuno Gomes, Dixon Etuhu and Colin Kazim-Richards as evidence of the support he continues to enjoy at boardroom level.
"I've spoken with Mrs Desai at length," he said. "There were some great conversations at the end of last season and she's been very supportive of us building a squad.
"I think everybody wants us to succeed, none more so than me and the players."
Murphy is fit to feature in midfield against Ipswich having missed last Sunday's friendly in Cork with a foot injury.
The former England international came out in support of Kean and revealed some of his team-mates sought discussions with Singh while in Ireland.
"Speaking on behalf of all the players, rather than getting into individual opinions, I think everybody was hugely disappointed at the content of what was said," Murphy said.
"Unfortunately I wasn't over in Cork, but some of the lads there had a meeting with him and expressed their opinions.
"What's been said will stay in house, but the lads certainly weren't happy about it and we are together, we stand by each other's side and we also back the manager."