But the Yorkshire side salvaged a precious point thanks to a hat-trick of super saves from German keeper Heinz Muller.
Muller - back after a nine-month injury absence - was on hand to deny Norwich as they created the best chances.
Barnsley fans were stunned when club skipper and last season's top scorer Brian Howard was dropped by manager Simon Davey.
The man who became a cult hero with a winning FA Cup goal against Liverpool at Anfield last season was not even on the bench.
But replacement Diego Leon had a sparkling start as the Tykes made a bid to end their miserable goal drought.
With just 37 seconds on the clock the Spanish midfielder almost caught out Norwich keeper David Marshall with an audacious effort from 40 yards but the keeper recovered to tip over.
And when Leon took the corner, Stephen Foster headed over before stand-in skipper Jon Macken went close.
Marshall had to be alert to hang onto a dipping shot from Leon, but the keeper was beaten by an angled effort from Jamal Campbell-Ryce only for Matty Pattison to clear off the line.
But after 13 minutes, Pattison was the guilty man when he handled in the area and gifted Barnsley a chance for a goal.
With regular penalty taker Howard out of the side, Macken stepped in and took a tame spot-kick which Marshall saved.
Another low shot from Leon skidded through a crowd of players and hit the post.
But the best chance of the first half came at the other end when Ryan Bertrand crossed superbly from the left and Antoine Sibierski produced super header, but Muller dived full-length to turn the effort wide.
Norwich saw further chances from a Dejan Stefanovic header and an effort from Pattison.
After the break, Iain Hume prodded a shot wide after Macken headed down and Barnsley defender Foster came close to an own goal with a crazy back pass that ran just wide.
After the break Norwich created the best opportunities despite the home side's impressive build up play.
But Muller was in defiant mood and tipped over a great dipping effort from Lee Croft and made another excellent stop to deny the same player.