The Dragons secured their first win of the season with a 33-15 bonus-point victory over Benetton Treviso at Rodney Parade last weekend but now face three straight away games against Scarlets, Edinburgh and Ulster.
The Men of Gwent have struggled on their travels in recent years, with their last away victory coming against Glasgow Warriors at Scotstoun in November 2013, a record Tovey is determined to put right.
And the 25-year-old is confident his side will reverse another unwanted trend as they search for their first win at Parc y Scarlets on Sunday.
"We've got to start winning four away games in a league season," the fly-half told the South Wales Argus. "We should be targeting the Italian teams and looking to pinch another couple.
"If we can do that then we would really push on as a region and start to become a better side. As soon as we get a couple of away wins the confidence would grow, we would know that we can do it.
"There are a couple of important games coming up against the Scarlets and Edinburgh and we need to win at least one of them to get a bit of momentum into the season.
"We've never won at Parc y Scarlets but we go there with confidence after last week's win against Treviso."
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