Deputy First Minister Michelle O’Neill was pictured among crowds at the funeral of Bobby Storey in June despite restrictions on public gatherings as part of the coronavirus regulations.
Ms Foster and Ms O’Neill have not made a joint media appearance after an Executive meeting since the row.
Ms O’Neill said the pair continue to deliver the same message even though they are not standing together.
Ms Foster said she wants to see acknowledgement from Ms O’Neill and Sinn Féin of the “damage” caused to public health messages being delivered by the Executive.
“It’s hugely frustrating for me that we can’t stand together and do that, but the Storey funeral has had an impact on our ability to do that, I hope that people will stick with the messaging that we are trying to give them, albeit in an individual way,” she said.
“I just feel that there needs to be an acknowledgement from Sinn Féin and the deputy First Minister that damage has been done.
“If that acknowledgement was there, I think we could then move forward and try to give the message out again. But at the moment there isn’t that acknowledgement that confidence was dented and the messaging was damaged.”
Ms Foster said there is a contrast between Sinn Féin’s attitude in the Republic compared to North, referencing the party's stance following the Oireachtas Golf Society event last month which resulted in the resignation of former Minister for Agriculture Dara Calleary and EU Trade Commissioner Phil Hogan.
“Sinn Féin pushed very hard in the Republic of Ireland to have people acknowledge there was wrongdoing in relation to going to a golf dinner, but I think we all saw the scenes in west Belfast in relation to that funeral and the fact that regulations and guidance were breached at that time,” Ms Foster said.
The First Minister added: “There are investigations ongoing both at a police level and an Assembly level as well and we’ll have to see the outcome of all of that.
“But I think it would help if there was an acknowledgement that there has been damage done to confidence and to messaging in and around Covid-19.”
