Pressure groups have grown increasingly disillusioned with the running of their club and are expected to voice their displeasure during Saturday's home date with Nottingham Forest.
Oyston, who has seen the Seasiders go 13 games without a win, is of the opinion, however, that everyone should be pulling together at a tough time rather than looking to create scapegoats.
He told the Blackpool Gazette: "No amount of chanting, demonstrations or anything else will have any influence on the decisions I make or the way I run the business. It just won't.
"If people need to do something and want to demonstrate or chant, then that's a matter for them but it won't have any influence.
"I'm all for positivity and supporting the team, and I think that's what people should do.
"If people want to have a discussion about that, then they have the route via the Blackpool Supporters Association.
"I'm happy to sit down soon with BSA and talk about where we are and more importantly how we get out of this.
"The only thing we can do now is stick together and get out of this situation."
Oyston, who has parted with the services of boss Paul Ince, added: "It frustrates me that we find ourselves in this position again, very much so. Throughout my tenure I've always majored on stability. We've really not had any lately.
"Football is a results business and we would not make a managerial change unless we had to. In this case we felt we had to. It's that which has given us the instability. The off-the-field side of the business is stable but on it we've had a nightmare run."
Blackpool impressed early on in the season despite working with a small squad and Oyston believes they should be looking to get back to those levels after adding seven fresh faces to their ranks in January.
He added: "Now we have to make sure we get the best out of the squad we have.
"Thanks to the changes we made in the transfer window, the squad can no longer we considered too small.
"We now have the basic tools to do the job, with sufficient quality and experience."