Guy Noves' side are reeling from their shock 30-3 drubbing at Ulster last weekend and Smith knows they will be desperate to banish memories of that performance - at Irish's expense.
"We showed spirit in the last 20 minutes against Llanelli in our opening game," he said.
"We'll need to produce that over an entire 80 minutes if we are to come away with anything from Toulouse.
"Guy Noves and his team will be smarting from what happened to them in Belfast and we expect to feel the backlash.
"They have an immensely talented group of players."
Irish have been lifted by the return of Riki Flutey and Kieran Roche who go straight into the starting line-up in two of five changes made following the 32-25 defeat by Llanelli.
Ireland lock Malcolm O'Kelly has demanded Leinster build on their victory over Gloucester when they face Edinburgh tomorrow.
A 37-20 triumph over one of the Guinness Premiership's form teams underlined Leinster's status as one of the Heineken Cup's favourites.
"We have been close in the past and we have just got off to the best possible start to this season's campaign," said the 32-year-old.
"We know we are in a difficult group and tomorrow's match against Edinburgh is going to be crucial.
"They have changed their style of play and are a very difficult team to play against.
"Two out of two is obviously the aim, and it would be a fantastic boost for us, but we know we are going to have to be at our very best tomorrow.
"Then, of course, we've got to play back-to-back games against Agen, which will be tough."
Girvan Dempsey will make his 50th Heineken Cup appearance for Leinster while Scotland international Chris Paterson returns for Edinburgh.
Martin Corry has vowed Leicester will not "fold" as they prepare for tomorrow's must-win clash with Cardiff.
The Tigers opened their Heineken Cup campaign with a 21-19 defeat by champions Munster at Welford Road and Corry knows they must triumph in the Welsh capital to keep their tournament alive.
"The winner of our group has got to go five and one to reach the knock-out stages. We have had our one loss - now we've got to win all our remaining games," said the England back row.
"We aren't going to fold. We know exactly what we have to do."