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Northampton have never played the French giants, who won the Heineken Cup in 1996, and have a miserable record across the Channel - winning only one European match in France in the past seven years.
"We have got a starter's chance," a less-than-optimistic Smith said. "I think we've only won once in France, so it's a big ask.
"Toulouse play a style of rugby that we don't come across too often. The play with a lot of continuity and they pass before contact - if they put it together on the day, they destroy teams.
"They've got the likes of Isitolo Maka out injured, but French teams don't have a salary cap - or not much of one - and they have a much bigger squad from which to choose quality players."
Smith said Toulouse were the last team he wanted to draw in the quarter-finals, but it was simply a glitch in an otherwise excellent season.
"We're pleased with what we've achieved this season," the former All Blacks coach said. "We've made the play-off stages in all three major competitions - and we're the only team in England to do that - but that in itself takes its toll.
"It means we've got a lot of hard games to play and it makes it tough. We were really going for a home quarter-final in the Heineken Cup and we topped our Pool, but it was too tough a Pool to get enough points for the home match.
"The Wednesday after the Toulouse match, we have to play Bristol in a Premiership catch-up match so there is no let-up."
The first of the three competitions - the Powergen Cup - ended in misery for Smith and his men with a 22-40 loss to Gloucester in the final at Twickenham on Saturday, after leading 22-20 at the break.
"They're a good team, Gloucester," he said. "We put ourselves in a position to win it, but we blew it. The boys put a lot into the game and they're going to be pretty sore this week."
Smith, who won 17 caps at outside-half for the All Blacks in the early 1980s, has no regrets about leaving his native New Zealand to take over the reins at Franklin's Gardens.
"It's a great club. I'm really proud of what the guys have done this season, and they're still building - we'll get even better.
"There's a great spirit here - good character, good people and a good work ethic. People point to our stars - the Cohens and the Dawsons - but everyone has gelled together and everyone gives 100 percent."
