Luke Amos scored a brace for QPR with Ilias Chair adding a stoppage-time consolation.
Struber said: "I'm very, very happy for my team and also for every Barnsley fan. I think this was a very important game for us to create a good performance and also gain important points.
"It was a very difficult week and in the end we have four points. My players create together a very good game with a big engagement.
"It is our big challenge to stay in the league and I see today the mentality is not like a relegation team, which is very important for us.
"We must work very hard in the next week. My 'to do' list is long but step by step we get better in our process.
"We have to deal with our defence in the next week. I have a plan for the next week over what we need to do to get better in the defence.
"I am happy and we have a few days free time now, which is important when you're in this difficult situation."
Barnsley remained bottom of the Championship standings but are now four points from safety.
QPR manager Mark Warburton was frustrated with his side's defence.
"We can't defend like that. We've been really solid for three games," he said.
"We went to Derby and got a point when we should have had all three and had a good result against Preston and a good result against Birmingham, but we've come and let ourselves down today, it's as simple as that.
"We've had a few heated words in the dressing room so I haven't seen a replay of the penalty yet and it wouldn't be fair to comment yet. Our players were not happy, but I'm not sure any player would be happy to give away a penalty.
"We had a chance to win 10 out of 12 and move to within a point of the play-offs.
"We knew that Barnsley would be a team scrapping for their lives, with young, hungry players. We spoke as a group about what we would face today.
"It's a tough place to come to and we had to meet that challenge. We knew we'd create chances and it could have been seven-all. We can't give away soft goals and expect to win."