Adams thumped in from 25 yards after just 14 seconds but Reading hit back through Adam Le Fondre and Noel Hunt before half-time.
Le Fondre then struck again from the penalty spot as the Premier League side ran out 3-1 winners.
Adams told the club website: "It was definitely the best goal of my career in terms of the strike itself and the importance of the game.
"I got the ball and they sort of backed off so I thought 'why not?' It was great to see it go into the top corner and the Broadfield was absolutely buzzing at that point.
"We lost goals at bad times when we were on top. We could have scored two or three before their first and then they got a second just before half-time.
"We feel very harshly done by for their third - the penalty - but I think the lads can be very proud of their performance.
"We are never going to win the FA Cup so this was a bonus game for us and I thought we did extremely well against some top players. The fans were magnificent too and I hope those that came for the first time come back and get behind us in the League One games."