Fiachra McGuinness made the comments after DUP leader Arlene Foster refused to be drawn on the contribution his late father made in bringing the championship to Royal Portrush.
Sinn Fein MEP Martina Anderson accused Mrs Foster of being “incapable” of acknowledging the role the former deputy First Minister played in securing the event.
Referring to a DUP tweet which included a picture of Mrs Foster at a press conference to announce the Open and which did not include Martin McGuinness although he was there, Foyle MP Elisha McCallion said it was “bitterly disappointing [Arlene Foster] unvalued his hard work …. and would rather try to erase his legacy”.
She said those types of sentiments needed to stop in order for agreement to be found in the Stormont talks.
The championship returned to Northern Ireland after a near 70-year absence. Organisers did not consider Northern Ireland as a venue over the decades the Troubles raged on.
On the BBC NI’s Sunday Politics the DUP leader was asked about the late Martin McGuinness’s absence given his contribution in helping to bring the tournament to Northern Ireland.
Mrs Foster said she was “sure there were many people that would have loved to be here, but unfortunately can not be here”.
“But for Northern Ireland the legacy this will leave will be immense,” she said.
Mrs Foster and Mr McGuinness were first and deputy first ministers when it was confirmed Portrush would host the event this year.
Asked if the legacy of the Open was a testament of what the DUP and Sinn Fein can do when they work together she hoped it would help restore Stormont’s power-sharing institutions.
“Things have changed absolutely and we really regret that we have not been in government for two-and-a-half years,” she said.“The position of my party is we should have been in government right through that time and if there were issues that needed to be solved it could have been dealt with in parallel talks.
“Of course Sinn Fein took a different position and pulled the government down.”
She said “serious negotiations” were continuing between the parties.
“Of course it is odd we don’t have a government we need to get the government back up and running again,” she added.
Ahead of the first round of The Open, Michelle O’Neill paid her tribute to the role Martin McGuinness played saying he worked “tirelessly” on the project.
“I want to commend all that have worked to bring this prestigious event to our shores,” she said.