The Reds tested home goalkeeper Willy Caballero numerous times throughout the match and missed chances in the first half, but the hosts eventually ran riot after being gifted goals by Marcel Ritzmaier, Alex Mowatt and Michael Sollbauer.
Struber said: "We expected a big opponent, with every player who has special ability. Nevertheless we had moments in the first half. We had 20 minutes completely in our hands and we have good chances but we cannot use those chances and this is our biggest issue at the moment.
"If we can take these chances, the game goes in a different direction. We helped Chelsea with three goals. In the second half we did not have the right intensity or aggression.
"We can speak about the mistakes or we can speak about the first 35 minutes. We created very good moments, especially in the first half but the mistakes made it very easy for Chelsea to score goals with our behaviour. The pressure in the second half was difficult for us and we were on the limit from the physical side."
Barnsley now host Coventry City in the Championship on Saturday. Struber said: "Now it is back to our daily business of the Championship. We have many learnings from the Chelsea game and we can develop our style a little bit. I hope we can play a good game on Saturday."