“Following the weekend’s result, we have had conversations as a group about how to move forward. We continue to work tirelessly in our quest to improve our performance and achieve the results we need on the pitch.”
Gray formally took over during the close season after four terms in the interim role, including a brief stint late last term following the departure of Nick Montgomery.
The former club captain, 36, has won five of his 17 games in charge so far this season, the last of which came against St Johnstone on September 14.
Bournemouth owner Bill Foley previously made it known that his Black Knights group did not approve the appointment after acquiring a 25% stake in the club.
However, Hibs added: “Through this difficult time, we support our head coach, David Gray, and his management team. All departments are under pressure to deliver.”
“We recognize that this is a difficult time for our fans and we know we can do better. Together, with Black Knight Football, we are working hard to make that happen.”
Following Saturday’s defeat, Gray said he “fully believes” he can improve the club’s form.
“I don’t think fear is the right word,” he said when asked if he had any concerns about his position.
“I completely understand the question and I am justified in asking it because of the situation we find ourselves in. The position we find ourselves in in the league is unacceptable.
“I have said it for several weeks. There were many excuses we could have used, but today I have no excuses for my performance in the first half.”
Hibs return to Premiership action following the international away to Dundee on November 23.
