However, Rees was far from happy with aspects of the region's performance at the Liberty Stadium.
The Welsh side scored four tries through Hanno Dirksen (two), Eli Walker and a last-minute Ashley Beck effort, but were forced to snuff out a second-half comeback by Treviso which saw them score two tries in as many minutes.
"It wasn't as comfortable as the result looked on paper. Definitely not," Rees said after the 38-17 triumph.
"There were periods in that game when we weren't in control of what we were doing and we put ourselves under pressure.
"We are pleased we regrouped and it was an inner spirit that got us out of trouble and they had to fight for the cause to get the two tries in the final quarter.
"First 20-25 minutes we built a healthy lead and then (the players) took their eye off the ball. I think we were chasing something that wasn't there and that was disrespectful to Treviso."
Ospreys captain Alun Wyn Jones said he was happy with the way his side kept their composure towards the end of the game when they were chasing a bonus point.
"We are pretty pleased with the performance - still a bit to work on. We have got to be able to think a bit quicker and not play so wide too early," he said.
"We can be pleased with the end result and the most pleasing thing for me was the composure we showed in the last minute, minute and a half.
"In the past you would have seen us tighten up in that situation but we realise that these pool games will come down to the last minute."
Treviso coach Franco Smith admitted his side produced a nervous performance.
"Obviously disappointed but we were beaten by a very determined side," he said. "We always anticipated that would be the case when they lost away to us at the start of the season.
"And everyone makes a step in this competition. We found our feet in the second half but we made a nervous start when we were falling off tackles.
"We were nervous and we want to prove that we are competitive at this level."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.