Wolves outscored their local rivals by 22 points to 12 to record their first win in St Helens since 1994.
"Let's talk about [the home match against league-leaders Wigan Warriors on] Saturday later," said Smith. "I'm happy to talk about this game and it's important we do. We're still in St Helens mode.
"We've had to suffer at the hands of St Helens quite a bit so we want to milk a little bit of this before we go onto the next week.
"We had a pretty dismal record at Knowsley Road, we've got a pretty good record here and we want to get the most out of that."
Warrington currently sit three points behind Wigan in the Super League table with three regular-season matches remaining.