Leigh Halfpenny's penalty had put the tourists 19-17 ahead with just nine minutes to go but Wales were ultimately left to rue their own ill-discipline at the breakdown, with Berrick Barnes nailing the decisive kick to give the Wallabies the 3-0 whitewash.
"We had our chances but fair play to Australia. They had chances and took them well. They kicked their points," Lydiate told Sky Sports.
"I can't really talk at the minute, I am just absolutely gutted."
The narrow defeat comes after Wales conceded a last-gasp penalty to lose 25-23 in the second Test, meaning their search for an historic first win over the Wallabies in Australia since 1969 continues.
"We're getting closer but it was our last chance today but it wasn't good enough," Lydiate said.
"Too many errors on our part but credit to the Aussies, they're a good team.
These games are won and lost by one or two points but we'll get there and we'll look forward to the autumn series at back at our place."
Australia captain David Pocock knew there would be little to separate the teams following the two previous encounters.
"After two games both teams had probably done their homework and knew what was coming," the flanker said.
"They put a lot of pressure on us at times but there weren't a lot of holes in defence.
"We knew in the last 10 minutes we had to get field position and hold onto the ball down there and we managed to do that. I am really proud of the way the guys finished the game but it probably wasn't the performance we were after."
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