Certified GKH Gardening Expert
Yes, you can use a fungicide to get rid of the mushrooms. But, you will want to have your soil's pH checked. It is probably low and this is why the mushrooms are growing.
Your lawn should have a pH of about 6 - 7. If it is lower than that, moss and mushrooms will grow because they like a lower pH. We would recommend that you get the soil tested before increasing the liming though. It may be the tree roots in the area are are causing the problem. You might also try applying a fugicide to the soil.