The Giants, a point ahead of the Wolves in Super League, had high hopes of ending their seven-match losing run at the hands of their opponents but they were blown away by the home side's flying start.
Warrington never looked back after establishing a 20-0 lead after 25 minutes and clinched a semi-final clash with Hull after winger Joel Monaghan scored tries either side of half-time.
"It was a good performance all round," Smith said. "I thought our defence was outstanding right from the off and we showed some good skill and scored some really good tries.
"We knew Huddersfield would have a real shot at it and we had plenty of people tell us that too so it fuelled the fire. We did a pretty good job for most of it. There was a period when we got a bit sloppy but I like the way we responded."
Former Huddersfield captain Brett Hodgson was once more the scourge of his old club as he recovered from a head knock to play a key role in the victory, as well as kicking six goals. "It was one of his best games this year," Smith said. "He was terrific at the back."
Huddersfield briefly gave themselves hope when quickfire tries from Shaun Lunt and Dale Ferguson enabled them to cut the gap to eight points but they paid a huge price for a series of handling errors and trailed 44-12 until Jermaine McGillvary and Scott Grix scored late consolation tries.
Giants coach Paul Anderson admitted his side had saved one of their worst performances of the season for their biggest test. "We never gave ourselves a chance," he said. "When you play good teams, you have to play well but we saved our worst for the best.
"At the start of the game we completed three out of 12 sets and found ourselves 20-0 down. When we had a period where we went six out of six, it became 20-12 but Warrington went away and scored a try just before half-time.
"I still felt we could compete and get ourselves back in, but the first time we got in a position to score we dropped the ball. We got taught a real lesson of intent today. It's a simple game and they ran harder than we did."
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