Ben Stokes and Pat Cummins' sides were ruled to be two overs short of the target after time allowances were taken into consideration, with match referee Andy Pycroft imposing the sanction.
The ICC said Cummins and Stokes pleaded guilty to the offence, and there was no need for a formal hearing.
"In accordance with Article 2.22 of the ICC Code of Conduct for Players and Player Support Personnel... players are fined 20% of their match fee for every over their side fails to bowl in the allotted time," the ICC said in a statement.
"In addition, as per Article 16.11.2 of the ICC World Test Championship playing conditions, sides are penalised one point for each over short. Consequently, two World Test Championship points will be deducted from both teams' points total."
Australia skipper Cummins sealed a remarkable two-wicket victory for his side in a thrilling climax to a gripping five-day battle in the opening test at Edgbaston on Tuesday.
