However the loss of back row forwards Robert Barbieri and Manoa Vosawai to the sin bin proved decisive as Toulouse ran in three second-half tries to record a 33-21 win.
But Smith admitted he was frustrated about the lack of respect given to his Treviso side and is adamant they are not simply there to make up the numbers.
He said: "A lot of people were just wondering how many points we would lose by but this squad has worked very hard.
"The only people who believed in us was us, we know what we can do. I am disappointed in the end that we couldn't finish it off. But the only points they scored was when we had one or two men fewer so they can't complain about the referee.
"We deserved better and it was only in the second half where their scrum was better when we had men off."
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