Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
The under-pressure chairman once again had to witness fans calling for him to resign after a shock exit from the Capital One Cup at the hands of League Two outfit Shrewsbury.
And these latest protestations come after new manager Riga publicly demanded more from his chairman when looking at targets to strengthen a squad in dire need of reinforcements.
However, Oyston believes he is doing all he can, and the club can turn their troubles around.
"Despite the accusations we are absolutely doing our job at the club but we need to be put in a position to sign players,” Oyston told the Blackpool Gazette.
“There’s a lot of negativity around the club at the moment, some I understand and some I simply won’t accept.
“I’m fully aware of the situation we are in and of course us making the worst start for more than 100 years alarms us.
“But the statistics are largely irrelevant, what’s more important is our current position which I would have expected to have picked up by now.
“We can no longer use the excuse of not having a pre -season as we’ve played the games now, the players should be up to scratch now.
"I don’t think the air of negativity around is helping."
Oyston, however, understands fans' discontent, after the club have endured their worst start to a season in 116 years.
"I understand their frustration, that’s only natural, I mean around the management and the manager," Oyston added.
“The manager is the one person who needs to be positive and I don’t understand the leader of any group or organisation being so negative.
“I’d sooner we are all positive and work as hard as we can to improve."