Despite losing their fourth game in five, Turner is adamant the Dragons are continuing to make progress in the absence of captain Tom Willis and Wales internationals Gavin Thomas and Luke Charteris.
"The players are disappointed, but I still see this as a major step forward," said Turner.
"Given the situation with players out through injury, I feel we can build on this.
"They are a powerful side and we were dealing with a lot of big Italian and South African internationals.
"They were a bigger side than us and they shoved us a bit on their ball.
"Treviso coach Franco Smith was impressed with the way we tried to play, but at 13-13 with a line-out in their 22 you need to grind out a win.
"We were in their 22 near the end trying to get a draw out of it, but it just wasn't to be."