"Zebre, like us, didn't have a great opening. But I've watched them in their pre-season games against two quality sides Northampton and Perpignan," said the former Ireland out-half.
"They are a completely new team in their attack and it will definitely be a challenge for us as their first visitors."
The weather conditions in Italy will be very different to the wet and windy Sportsground from last Saturday. It is hot and humid in Parma with expected temperatures of 31 degrees for Friday.
"Against the Blues we weren't tested too much on the defensive side of things as the weather wasn't conducive, but certainly Zebre will ask questions of our defence."
The frustrating 13-9 loss to the Blues, during which Connacht failed to cross the try-line, was not the game or the result that Elwood's men were looking for.
Speaking after the round 1 clash, Elwood commented: "It's disappointing in a home game, dominating a lot of the territory and plenty of possession and to come away with a losing bonus is not really acceptable in a game which we would have targeted.
"It's three points lost but in fairness to Cardiff, they dug it out and took their chances. We had plenty of possession but we had 11 turnovers in the opening half and that put us under pressure.
"We just could not hold onto the ball. That high level of turnovers was one of two major elements that let us down.
"The second was our kick chase game - that should have been better in order to exert pressure," he added.
Elwood singled out the set piece solidity of the Connacht pack as something to build on heading into match number 2 of the new season.
"We had a lot of dominance in the scrum against Connacht. If we're going to have that dominance in the set piece we have to make it pay, but it's an area of strength we want to bring forward to this week when we meet Zebre."