Grizzled Czech Soucek had a hand in West Ham going in front after 13 minutes when his flick-on went into the net off Forest defender Murillo.
But Forest levelled after the break through Nicolas Dominguez, then Morgan Gibbs-White tucked away the winner from the spot after being clattered by West Ham keeper Alphonse Areola.
Areola had been trying to intercept a ball into the crowded area but mistimed his punch and connected instead with the face of Gibbs-White and referee Tony Harrington awarded the penalty after a VAR check.
Defeat left West Ham in 18th place, seven points behind Forest, who sit one place above the relegation zone.
"For me, it is a joke. I just saw it again and I think we can have 20 penalties per game if it is like that," Soucek said of the incident. "I came to the Premier League because I thought it was the toughest league in the world and we are all fighters and warriors, but this looks more like basketball when you can't touch the player. This is what I saw."
"(Areola) came for the ball, I think I cleared it and that was already out. We didn't know why there was VAR and then the penalty, so it was tough for all of us."
West Ham are now winless in 10 league games and manager Nuno Espirito Santo is under severe pressure after only two league wins since taking charge in September, following his sacking by Forest three games into the season.
Soucek insisted the squad were still fully behind Espirito Santo but admitted West Ham were in big trouble.
"We have so many games but we have to do it from the first game. Now is the time. We have to be winning. Seven points, we cannot just win one or two, we have to win a few in a row," he said. "I still believe and will until the end, but I have to say that we are in a really bad position."
"We will look to the mirror and know the position we are in. Nobody from the squad wants to play second division."
