The 26-year old German striker, who joined the Tigers from SC Paderborn last summer, was being linked with a move away from the KC Stadium in the recent transfer window following the arrivals of Danny Graham and Yannick Sagbo.
However, Proschwitz is keen on proving to manager Steve Bruce that he is an integral part of the squad as he looks to kick on from his winning goal in Tuesday's 1-0 Capital One Cup win over Huddersfield Town.
"I don't care now at what's gone, I'm just looking at the future," Proschwitz told the Hull Daily Mail.
"I decided to stay and fight for my opportunity and I hope my chance will come to play soon. Hopefully I can score then too.
"I came here to play in the Premier League. The first month of the season wasn't easy for me but I don't want to quit and I don't want to give up.
"First-team football is where I want to be and I believe I performed quite well.
"It hasn't been easy but I decided to stay and work for my chance. Hopefully that will come soon.
"I've had a few games for the reserves, a few very good performances with loads of goals, and I'm happy that I could help the team."