The Dutchman finds himself under immense scrutiny following Barca's recent results, having suffered a 3-0 home defeat to Bayern Munich in the Champions League followed by a 1-1 draw against Granada on Monday.
He has also been linked with an exit from Camp Nou, but Koeman insists the club stand with him and understand that he needs time to get the team challenging for major trophies again.
The 58-year-old addressed reporters at a press conference on Wednesday, but left before they had a chance to ask him questions. He read out a statement that said: "The club stands with me as the coach in a situation of rebuilding.
"The financial situation of the club is connected to the sporting activities and vice versa. This means that we as a team have to rebuild without having to make any big financial investments. This needs time.
"The young talent today could end up being the next big world stars in just a few years. In order to reconstruct this team, young players must get opportunities like Xavi and Andres Iniesta had in their day. But we must ask for patience.
"What's more, being in another ranking in La Liga is a great success. This is a great footballing school for these talents. In the Champions League we can't hope for miracles. The defeat to Bayern Munich last week has to be viewed from that perspective.
"The process that we're in right now, the staff and team deserves unconditional support in word and in actions. I know the press recognise this process. It's not the first time in Barcelona's history that this has happened. We count on your support at this difficult time. Us, as a staff and the players, are very happy with the great support from the fans like we had in the match against Granada."
Barcelona president Joan Laporta, too, sent a desperate plea to the club's supporters, asking them to "stand by" the team. He insisted that the club knows "what needs to be done" but pleaded with the fans to "remain calm" and to "back their team".
Barca have made their worst start to a LaLiga season since the 1987-88 campaign, and have won just four of the opening 10 games under Koeman.