The quarterback, who regained the starting job after Brian Hoyer tore a knee ligament earlier this month, threw two interceptions and was sacked twice during the AFC North side's 31-17 loss to the Detroit Lions.
The 30-year-old told the team's website: "You play the quarterback position at any level, those are the questions you've got to answer. Winning's the cure-all.
"If we can win games, that cures everything. I need to do my part. I need to be more consistent to help this team in whatever way possible.
"Once we get in here, especially today, it's all behind us. It's on to Green Bay and we're not looking back. No loss is ever easy to shake off. You've got to have a short memory and move onto the next week against a good football team."
Head coach Rob Chudzinski has also called for Weeden to cut out the errors.