I was feeling the same way when I started playing weekly soccer pickup games. Like you said, I think a big part of it is the adrenaline and nerves at the start of the game. After about a month I was no longer getting as winded. Part of that was probably conditioning and part was just feeling more relaxed on the field. I would say make sure you're keeping the intensity high during your weekly sprint sessions to try to duplicate the cardio demands of playing (i.e alternating between sprinting, jogging, and walking) and then also stay calm and don't put too much pressure on yourself to be perfect while you're playing. Focus on having fun and I think the conditioning should take care of itself.