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.
Town boss Johnson contested referee Trevor Kettle's late decision and believed his side more than matched the former Premier League outfit.
Johnson said: "If the referee gives that as a penalty then he should have given one for us too.
"Our boys were magnificent today and they deserved more than they got. We outplayed a very good Reading team and our boys did everything but score.
"We kept creating chances and had lots of shots, and when they were on target the keeper made some good saves. I'm not sure you can do any more in a game and get beaten.
"We respect the opposition and think they are still one of the favourites to get promotion, so we're pleased that we competed more than adequately with them.
"I suppose that's why it's even more upsetting when it gets taken away from you by something out of your control.
"I think we've found our Championship legs over the last couple of games, and I hope that bodes well for the near future."
Reading manager Nigel Adkins hailed his side's valuable away victory which came after a 6-0 thrashing at Peterborough in the Capital One Cup in midweek.
He 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."