The 49ers triumphed in overtime to secure their first win in five games by beating Bears 26-20 at Soldier Field, a result which moved them to 4-8 for the season.
The victory was the 49ers' first on the road this season, and Bowman was pleased to see his teammates dig in and overcome their poor form to secure the result.
"Today was a chance for us to not go out here and act like we threw in the towel, but let this affect the years to come and for the young guys to know that this is the NFL. You are going to lose, and you are going to win, but you have to continue to play all 16 games," he told the franchise's official website.
"I think that today showed what we have been trying to get to, to just keep fighting no matter what happens in the game and let that decide who wins the game. If you let the adversity affect your play, we would not have had a shot like we did today.
"I think that we are starting to get the idea of what really makes a good football team and that is guys just doing their jobs. I really see that we can have something special here. Maybe it did not come as fast as we wanted, but we can definitely see the process and it is looking good for us."
The 49ers next face a clash with the Cleveland Browns next Sunday.