Synchronised - the Cheltenham Gold Cup winner, and many people's favourite for the National - and According to Pete both fell at the famous Becher's Brook fence and had to be put down following fractures to their legs.
The incident marred what was otherwise a thrilling race, won by Neptune Collonges in the tightest ever Grand National.
"We are desperately sad at these two accidents and our sympathies are with the connections of both horses," said Thick.
"When a horse gets hurt, everyone is deeply upset. Safety is the first priority for the organisers of the Grand National and we make every effort to ensure that everyone involved in the event is able to participate in safety.
"After today, we will, as always, be looking at all aspects of this year's race to see how we can improve safety further."