Treviso lie ninth in the table with their last-minute loss to Ulster two weeks ago ending any hopes of reaching the top four come May.
The Italians were hit hard by Six Nations call-ups and are winless since Christmas, a sequence that has seen them slip down the table.
But with three RaboDirect PRO12 matches remaining Smith is demanding they toughen their resolve.
"From our point of view if this season were a match then there's only three minutes left and we want to keep fighting with the same intensity other squads have as they fight for the play-offs," he said.
"Our aim is to finish as high up as we can.
"If we get a few victories we can still arrive in a high position.
"I don't want to pinpoint a position but we'll be going for as high up as we can.
"We'll try and keep up our principles of dominating the contact area, defending very well and playing with the ball in hand.
"We also need to have a high quality first-phase attack and above all we must try and win."
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