A 26-17 win over Cardiff Blues last weekend completed the clean sweep of wins for the Italians who have now beaten every team in the RaboDirect PRO12 since first joining back in 2010.
Smith's side have won their last four home games in the RaboDirect PRO12, their best-ever home run, but the head coach is not underestimating Connacht.
Eric Elwood's troops were three games unbeaten before their loss to Munster last weekend and Smith knows that fly-half Parks and his unerring right boot are a real weapon for the Irish side.
"Cardiff was not the most attractive match, even if it was a good one, but we had a lot of desire," he said.
"Connacht had won three or four in a row before last week and with Eric Elwood finishing this year after 26 years I think with the club, so they will want to finish well for him.
"They have a lot of character and desire, they beat us here last year 10-9 so it will be an important game.
"We have so much respect for Dan Parks and we know he kicks well and manages a game well. He arrived at the right time for them, but they have a lot of other players and they are well-balanced.
"It would be nice for the fans and the team if we had better conditions this weekend against Connacht with some sun.
"They have a lot of experience playing in wet conditions but the squad is very excited about the game. With the spring nearly here everyone is desperate to push on."
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