The win not only boosted the Tykes' spirits but also provided a much-needed boon to their points tally as they climbed off the bottom of the Championship table in time for Christmas, leapfrogging Wigan and Stoke to move one point behind Luton in 21st.
Patrick Schmidt's stoppage-time header sent the visiting fans wild and handed Millwall a rare home loss after Aiden O'Brien looked to have snatched a point five minutes from time when he cancelled out Conor Chaplin's deft first-half strike.
Struber was keen to highlight just how pivotal Schmidt's goal could be in the context of the relegation fight as Barnsley won away for the first time this season.
He said: "For us it's a very, very important victory, it's good for our soul, for our mind and for our self-confidence.
"We created a very good second half. In the first half we had some problems on the ball, our positioning was not clear and we gave away simple balls.
"But on the counter-attack we are very efficient and this is a big strength. In the second half we had more control of the ball and that was the key – the opponents had no control of the game.
"After the equaliser, we had the mentality to win and this is a special moment for me, for my team and the whole club.
"We didn't play like a relegation-threatened team, we played very well, and I hope we can follow that up on Boxing Day – for now, we'll have a merry Christmas!"
Chaplin, 22, beautifully diverted Jacob Brown's cross over Bartosz Bialkowski and into the far corner of the net after 39 minutes to give Barnsley the lead with his seventh goal in the last seven games.
Struber added: "He [Chaplin] is in top form, we're very happy we have Conor, we have so many good players, big talents in my team.
"Now we also have very good spirit and teamwork. This is the main thing to win games – the teamwork, character and discipline."
Unfortunately for the Lions, their best chances often fell to centre-back Jake Cooper – who headed wide on three occasions – and after just a second loss at the Den this term, boss Gary Rowett cut a frustrated figure.
He said: "I'm disappointed. The way the game ends you're always going to be frustrated and annoyed.
"We didn't play as well as we'd have liked. I thought for the first 38 minutes we were really good, just without that cutting edge at the top end of the pitch.
"It's similar to some of our other home games where we've had a really good opening spell, we just haven't scored the goal or created the clear-cut chances that the play deserved.
"That then puts pressure on you for the rest of the game. I knew it would be a difficult game, with so much expectation after such a good run of form, you always know there might be a banana skin.
"We probably would have been disappointed with a draw but we would half-accept it and we should have taken a point.
"Their winner is a little bit of naivety from us, not quite doing the right job in the right area. It's still a good header but it shouldn't come to that.
"I felt as though we've thrown a point away and that's our frustration."