The Tykes are now winless in 10 matches and have lost their past four in the Sky Bet Championship.
“I saw a Barnsley team that tried its best in a difficult situation to get the best result,” head coach Schopp said.
“When you are in a situation like we are right now, it’s not that easy.
“I don’t know how many times we tried to get in Reading’s box to finish well, to get a goal. But it just didn’t happen. It’s a film that we have already seen so many times this season.
“After 60 or 70 minutes, we had the situation when we were struggling in a certain position in the midfield and we had to make a substitution.
“At this moment, we lost for a couple of minutes our organisation and this was enough today for a team like Reading to beat us.
“We tried to get back into it, even in the last few minutes. But scoring for us is a really tough thing to do right now. We tried to go for it to the very last minute but we just couldn’t do it.
“Teams like Reading - and other teams - have that quality to take an advantage from this moment that we are having.
“We have already paid a lot in these moments this season. And today, again, we lost a game that we probably shouldn’t have lost.”
Although Barnsley dominated the first half, they squandered a series of good chances, most notably through Cauley Woodrow.
Callum Brittain also struck a post for the visitors early in the second period, before John Swift secured Reading’s win with a superb solo effort in the 77th minute - his eighth goal of the season.
It was also Reading’s fifth victory in six matches, and Reading manager Veljk said: “It finally worked for us.
“It was a well-deserved win and the team worked really hard and was really mature.
“We knew that at 0-0 at half-time, Barnsley were going to have more confidence and courage in the second half.
“Barnsley had a few opportunities then. That’s why it was a hard win today and a bit of a relief. At the end we tried set-pieces, we tried combinations, we tried counter-attacks and we tried over the top. And that’s how finally it worked for us.
“It was a very good job done, another clean sheet, another positive thing, and our confidence and mentality is being reinforced again. That’s my read of the game, even though Barnsley made it tough for us. In terms of physicality, that was one of our toughest games.”
Reading: Southwood, Yiadom, Moore, Dann, Baba, Laurent, Drinkwater, Dele-Bashiru, Swift, Ejaria, Puscas (Azeez 63). Unused substitutes: Camara, Rafael Cabral, Ehibhationham, Osorio, Clarke, Ashcroft.
Barnsley: Collins, Sibbick, Helik, Moon, Brittain (Cole 83), Palmer (Hondermarck 73), Gomes, Jordan Williams, Adeboyejo, Iseka (Oduor 67), Woodrow. Unused substitutes: Vita, Walton, Ben Williams, Frieser.
Referee: A Davies (Hampshire).