They produced one of the greatest upsets in the competition's history to stun heavily fancied Biarritz 7-6 in the quarter-finals, but domestically they are on the brink of disaster.
With just one game left to play in the regular Guinness Premiership season, they lie one point behind 11th-placed Worcester.
The contrasting fortunes mean Saints could experience the high of booking a place in the Heineken Cup final just six days before being relegated to National One.
But Smith is confident the squad are moving in the right direction following a nightmare spell at Franklin's Gardens and knows their growing confidence will be essential at the Ricoh Arena on Sunday.
"We're not short on belief. The enjoyable thing about this Heineken Cup run has been that the matches are just one-off games," said the former Scotland prop.
"They have given us a break from the league, allowing us to go out and express ourselves.
"The league is obviously, especially in our situation, completely different.
"One of the underlying themes throughout the build-up to the Biarritz game was that the most important thing to do was to enjoy ourselves, express ourselves and play for each other.
"There was no league position to worry about, no bonus point to worry about, it was just a case of going out there and doing it.
"The knockout aspect of the Heineken Cup has called for a different mentality.
"I'm not sure if there's less pressure, it's more a change of focus because of the change of scenery.
"We know we haven't played to our potential. It's disappointing to say that so far into the season, but we are improving."