Martin Canning is appealing for a united front as he prepares Hamilton for the crucial midweek home clash with Aberdeen.
The 2-0 weekend William Hill Scottish Cup defeat at St Johnstone prompted open hostility from a section of Accies fans.
However, the Accies manager was more concerned by claims that his father had felt it advisable to leave McDiarmid Park after a confrontation with critics which had attracted the attention of stewards.
Upset by first-half Saints goals gift-wrapped by stand-in goalkeeper Ryan Fulton to Jason Kerr and Tony Watt, visiting supporters appeared to squabble amongst themselves before order was restored.
Canning made it clear he could handle criticism but condemned a minority of followers for their behaviour, saying: "I can't accept it if my dad has been abused and it gets personal.
"But I am committed to doing my job for this club. I have a great relationship with everyone at the club.
"It frustrates me. It is a small club and we work really hard. We have competed for five years in a row in the Premier League and hopefully we are going to do it for a sixth.
"It's the most successful period in Accies' history post-war.
"We have a youth team playing in the Champions League, we have a great infrastructure and a board which is behind the team and the local community.
"In terms of what we are doing there should be positivity about."
But 10th-placed Accies are just four points clear of St Mirren in the play-off spot ahead of Wednesday's visit of the Dons.
Canning continued: "We all want to win more games than we are winning but I'm pretty sure Dundee and St Mirren want to win more games as well.
"It is difficult at the bottom end of the league. It's never going to be easy or plain sailing.
"We have brought in 16 players this season. We lost Michael Devlin, Ali Crawford, Greg Docherty, Lewis Ferguson and Giannis Skondras in the last 12 months.
"We want our fans to get behind the club and get behind the team."
St Johnstone manager Wright admitted his side had got off to the perfect start, with Kerr heading home within the first minute.
He praised striker Watt for his work-rate and finishing prowess, adding that centre Chris Kane had provided an ideal foil with his running game stretching the Hamilton defence and creating pockets of space.
Wright has also been impressed with the impact being made by former Hearts and Raith Rovers midfielder Ross Callachan, with Murray Davidson injured.
The manager added: "I thought Ross was excellent. His energy levels are incredible and he always looks a goal threat. He has set a really high standard."
