The defender completed a controversial move from Birmingham to West Ham in January, but injury has restricted him to just 41 minutes of action.
Upson has made good progress from his calf injury, but admits time is running out if he wants to aid the club in their relegation fight.
"It has been quite an intensive period and I think I am coming through the other side," he told Sky Sports News.
"I will not write off playing again this season, but we are running out of games and time and it looks slim."
Despite being restricted to just two outings in West Ham colours, Upson has no regrets about moving to the East End of London.
"I have worked hard to get the move here and be pleased with the situation, so to not be able to play given the position the team is in as well is frustrating," he added.
"It is difficult, but you look to solve the problem and get on with it rather than complain."
West Ham have battled hard to keep themselves in the hunt and Upson claims the mood in the camp is positive.
"The spirit is good and the team is in a very positive frame of mind," stated Upson.
