The Bolton boss endured fierce criticism from a section of the 1,163 travelling fans at Ewood Park during the second half as his side lost a record 28th game of the season.
Assistant boss Steve Parkin spoke to the media after the final whistle and when asked if Parkinson and his staff had considered stepping away from the job, added: “No – we’re as disappointed as they (the fans) are.
“We care about the job we have got, we care about the club, and it has been tough for two years.
“We shouldn’t hide away from the fact last season was tough, we survived by the skin of our teeth, and this season it has been even worse.
“It hurts us to see the team lose and it hurts us to see what happened at the football club. But personal pride and integrity means you have got to keep going.”
Wanderers have scored just 29 league goals so far and are almost certain to set a new record low for a 46-game season, which currently stands at 41.
They drew another blank against Blackburn, much to Parkin’s chagrin.
“We created enough chances to score more than one goal and managed to score none, which is disappointing for us,” he said. “We’d started the game nice and brightly.
“The one chance we gave their striker – who cost a lot of money – he tucked away. We didn’t manage to do that.
“The lads tried their best in difficult circumstances and I am disappointed to lose again but more so that we didn’t score. Callum Connolly had a couple of very good chances.”
Potential new owner Laurence Bassini was in the directors’ box to watch the game along with two representatives of the Bolton Wanderers’ Supporters Trust board.
It is understood he has made paying the players and coaching staff’s outstanding wages his number one priority in the coming days but is facing difficulties because club accounts are currently frozen.