The Reds had five of the six shots on target but could not make the breakthrough against their promotion-chasing visitors.
Struber said: “I am happy with the performance against a massive, physical opponent. My boys did a brilliant job, especially in defending set pieces. We had the right attitude.
“In the first half, we did not have the right control on the ball and we were not clear. But, in the end, maybe it is a very important point. Millwall are a very strong side and they play for the promotion positions. I can see that because they have very big motivation.”
Barnsley have now kept clean sheets in both of their games since the re-start. Struber said: “This gives everyone a good feeling. Our defensive structure is very good. The boys have a very high focus but we need more control on the ball and to find more chances. We had our big chance from Jacob Brown.”
Mads Andersen saw an effort saved in the 93rd minute. Struber said: “Mads had a fantastic game. He was so reliable in every situation but he had a big chance for us. In the end it is 0-0. I am happy with the performance and the result.”
Defender Ben Williams added: “Coming off the back of the win last week, we are a bit disappointed with a point. But it’s another clean sheet and it’s a point. We had chances, they had chances. We were unfortunate not to take our chance right at the end and win the game. We’ll take the positives and move on. It could be a big point.”
Luton, Wigan, Middlesbrough and Charlton won today, leaving Barnsley bottom of the league and four points from safety. Struber said: “The problem is the results of the other teams but this is not in our hands. We have no influence on other results. It is disappointing but we still have seven games and, when we bring the same performance as today, but a better attack like last week, it is difficult to play us. I have no time to cry, we have to bring a good mood and good attitude in our next game.”
Williams added: “We all checked the league table after the game and it is disappointing. But I have said all along that anyone can beat anyone in this league. We still fancy our chances to stay up. We are picking up points. Other teams are getting results as well but we just need to focus on our situation.”
The match was the first ever behind closed doors at Oakwell. Struber said: “To play without atmosphere and emotion is difficult and surreal in the Championship. But it is special times and we have special measures. Our players had very very good self-motivation.
“My message to the fans is: cross your fingers for us and give us our energy from your home. The boys are absolutely in a fighting mood to climb out of their relegation zone. I think we have many games and we have a chance. We need a big energy from our supporters.”
Struber took Elliot Simoes off at half-time, saying: “Elliot is a young player, the physical challenge is not so easy for him. It was a decision to protect him.”
Struber hinted at changes for Tuesday’s home match against Blackburn Rovers, saying: “It is the right time for rotation. It’s maybe better to go back to the diamond so we are more clear.”