McNamara saw his new-look side beaten as Billy McKay scored a first-half winner for table-topping Inverness to leave United still searching for their first win of the new campaign.
He said: "I think it's important to get the fans behind us whenever we play at home.
"But we were sloppy in a lot of our play and the players need to be brave. That was the most disappointing thing about today's performance.
"They need to take responsibility more because in the times we did that we passed the ball around and caused them problems
"But there was not enough of it which was frustrating for everyone."
McNamara saw new boy Chris Erskine booed when he was replaced by winger Ryan Dow in the second-half.
But the United boss insists former Partick Thistle star Erskine will prove to be a shrewd signing.
He said: "I know what Chris can do and that's why I brought him here.
"But that's football for you.
"The fans are as frustrated as the players but that's understandable as we all want the best for the club.
"You have to give credit to Inverness because they're a good side and Terry Butcher is doing a good job."
McNamara felt Inverness skipper Richie Foran could have been red-carded for his high first-half challenge on Gary Mackay-Steven, only for referee Steven McLean to caution him instead.
He said: "I thought it was a high challenge. I thought it could have been a red-card.
"But the referee deemed it to be a yellow-card and we just have to get on with it."
Inverness boss Butcher praised McKay, who also scored against St Mirren last week, for maintaining his momentum as he prepares to depart for international duty.
Butcher said: "Billy was great again.
"I think he deserves to get the chance to show what he can do for Northern Ireland against Russia in their World Cup qualifier in midweek.
"He buzzes around and is always in defenders' faces. He must be a real nuisance to play against."
He added: "I'm very happy with the start we've made to the new season.
"But that's all it is. We won't be getting carried away.
"It was a solid all-round display which I was delighted about.
"We would have won by more but we're happy with the three points."