Three penalties from fly-half Miah Nikora were all they had to show for their efforts as they lost 13-9 and Elwood was left frustrated at that return given how much of the ball his side saw.
In Zebre's first match in the RaboDirect PRO12 they were handsomely beaten 37-6 by Newport-Gwent Dragons at Rodney Parade but Elwood knows that they will be a different proposition on Friday night.
Connacht will be the first ever league visitors to the Stadio XXV Aprile in Parma and ahead of their trip to Italy Elwood urged his players to expect a testing reception.
"Zebre, like us, didn't have a great opening," said Elwood. "But I've watched them in their pr-eseason games against two quality sides Northampton and Perpignan.
"They are a completely new team in their attack and it will definitely be a challenge for us as the first visitors.
"On Saturday, we weren't tested too much on the defence side of things as the weather wasn't conducive but certainly Zebre will ask questions of our defence.
"We had a lot of dominance in the scrum (against Blues). However, if we're going to have that dominance in the set piece we have to make it pay.
"But this is an area of strength we will want to bring forward to this week when we meet Zebre."
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