In the first ever league meeting between the sides, Adam Le Fondre's penalty 13 minutes from time handed the Royals their first Sky Bet Championship win since the opening day and condemned the Glovers to a fifth consecutive defeat in all competitions.
Adkins said: "We're delighted with the three points and a clean sheet. You talk about performances all the time but we came away from home after a really challenging week with 2,000 supporters behind the goal and won, which is the important thing.
"After the week we've had, we asked whether we could go away from home again in what is our third away match in a week and win - and we did."
Adkins also revealed his decision to replace Gareth McCleary with Danny Williams in the first half was taken for tactical reasons.
"I want to win games of football," he said. "The substitution was nothing to do with Gareth, but we were far too exposed. We set up with an attacking formation with Gareth on one wing and Royston Drenthe on the other. They were playing a bit narrower and were getting a lot of the football.
"Do you leave it until something happens or do you try and do something about it? I made the decision to do something about it.
"The result and the performance midweek cast something over the club, but we've come away from home and done what we needed.
"Yeovil was always going to be a challenging fixture because we were expected to win."
- Sports & Recreation
- Adam Le Fondre