Edoardo Gori and then a penalty try allowed the Italians to move seven points clear with time running out, only for replacement scrum-half O'Donoghue to pop up at the death, with Dan Parks slotting the crucial conversion.
As a result Treviso are now certain to end the season seventh in the table, their highest-ever finish, and Smith believes there are positives to take from the game.
He said: "We didn't manage the game well at the end so there is disappointment. We needed to hold on to the ball. I have to say though that they deserve a lot of credit.
"They are a very underrated team, their defence in the first half was fantastic. They don't have lots of stars but they play with a lot of desire and we can't forget that.
"We could have scored with the chances we created and we're all disappointed with that. But we have a plan, we wanted to build in the second half and I think we did that getting to 23-16. In the end it was a good game of rugby and very even."
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