Lee said his team were always chasing the in-form Hockeryroos who took the lead through Jodie Schulz's 32nd penalty corner and increased their advantage with Georgie Parker and Karrie McMahon's second half strikes.
England will now face hosts Argentina in the bronze medal match after they lost on penalties to the Netherlands.
“I think all the teams that were in Pool A have struggled," said Lee.
"Our group have played in intense heat all week, in contrast to the Pool B teams who have played in the cooler evening matches.
"We looked physically very tired and ended up chasing the game for most of the match.
"I was really pleased that we kept at Australia and never gave up, but they were the better side, as they have been all year, and they deserved the win.”