The Hammers meet Forest sitting inside the bottom three and having lost at bottom-of-the-league Wolves on the weekend.
Soucek told the club's website: "We need to fight for everything, and show a real determination to get out of this current situation.
"We have high-level players, and I’m confident we have the tools we need, but we need to keep pushing and show determination in training and out on the pitch.
"There are going to be good and bad moments, and that happens even when you’re doing well. We’ve shown flashes of what we’re capable of, and we just have to put a proper run together now.
"I know I have a responsibility as a leader in this group, and I’m going to give everything I can to help the team.
"I think my role has changed in the six years I’ve been here, because people didn’t even really know me when I first arrived!
"Along with the likes of Jarrod (Bowen) and Łukasz (Fabiański), us three have been here a long time, and we have to be involved with everything and help the team.
"The team has heart, and we’re all desperate to deliver for the West Ham United fans, who back us through everything."