The loss was the Accies' fourth in a row and extended their winless run to 15, consigning them to the bottom, five points from nearest rivals St Mirren.
Aberdeen boss Craig Brown was happy with the win and the way his side has turned their form around recently but suggested that sixth-placed Inverness maybe a bit too far out to catch.
"I think the top six is an unrealistic goal and a bit too much of an ask. However, while it is mathematically possible we will not give up and we will be fighting to get there," he said.
"If we got there it would be a terrific achievement. I'm pleased with the distance we have got from where we were but I'm not going to start talking about the top six.
"I can't comment about the attitude they showed at the start of the season but I do know that they are determined now.
"Even in the games when we were down against Celtic, they maintained a favourable attitude and they still have that positivity. There is a determination about them, which is pleasing to see."