Grant's side were unable to break down their Championship opponents in front of a woeful 11,214 crowd at Fratton Park and following the game a large group of home fans besieged the directors' entrance in Frogmore Road, chanting 'sack the board", 'where's the money gone?' and "where's the owner of our club?'"
With Pompey facing a winding-up petition from Her Majesty's Revenue and Customs in the High Court, a transfer embargo and a struggle to pay their players for the third time this season, Grant can understand the fans' frustration.
He said: "I'm very impressed with the supporters. They were behind us for the whole game and it's not an easy time for us generally or in this game. I respect them.
"I understand (why they are frustrated) but you must understand that no-one at the club is happy with the situation.
"My job and the players' job is to do things on the pitch.
"The situation is not easy but we can do our best for the team on the pitch and that's what I will do."
Grant has spent more time discussing the club's financial plight than his players' efforts on the pitch since taking over as manager from Paul Hart in November.
The former Chelsea boss, who once had Russian billionaire Roman Abramovich's vast fortune at his disposal, admits this is getting increasingly tiresome.
He said: "To be honest, I feel as if I'm not answering as a football manager.
"Eighty per cent of the questions I have been asked since I came here haven't been about the football.
"I like to talk about things on the football side, but what can I do?
"This is the situation and if I have to answer these questions, I will answer these questions.
"But there are enough problems on the pitch we need to take care of."
Meanwhile, Coventry boss Chris Coleman was disappointed to see his side's concentration wane just before the interval.
Richard Hughes was given ample time to fire in an inch-perfect cross from the left-hand side of the box and Boateng nodded into the net unchallenged.
But the Welshman feels his side leave Fratton Park the happier of the two teams.
He said: "It will be a better result for us than Portsmouth with their current situation.
"I think, on the balance of play, it was a fair result. I thought we did well and we coped well when we had to.
"We were disappointed to concede when we did - a minute before half-time. That's two games running this lack of concentration has let us down.
"I was very pleased with the lads - I thought they applied themselves really well.
"We knew it was going to be difficult. They're a Premier League team.
"Avram fielded his strongest team, so that paid us some respect. But it was a good result for us."