The Zimbabweans have so far drawn a blank ahead of the second Test in Dominica, which concludes their visit to the islands. West Indies whitewashed the tourists in the preceding Twenty20 and one-day international series before last week's nine-wicket win in Bridgetown maintained their dominance.
"Every game is important. We want to make sure the Zimbabweans don't win a game on this tour," Radford told the West Indies Cricket Board's official website.
"We want to send them home empty-handed. We have had a really good run in Test cricket this last year - we did well against New Zealand, we did really well in Bangladesh and we would like to follow that up with a complete sweep here as well."
Victory in Barbados was the Windies' fifth in a row in Test cricket - a feat they had not previously managed since 1988 when they were at the top of world cricket.
While the current team is ranked down in seventh place in the International Cricket Council Test rankings they have shown signs of climbing the table during the past 12 months.
With Darren Sammy at the helm of a developing team, they swept New Zealand and Bangladesh 2-0 at the end of last year.
That followed 2-0 defeats to both England and Australia when, especially against Michael Clarke's team, they proved they could stand up to the top-ranked nations.
"There is a lot of confidence in the team and there is a good combination of youth and experience in the squad," Radford said. "It is great to have the young and the senior players playing alongside each other. Any side we come up against we want to perform well.
"There is a real thirst among the players to keep improving and it's nice to have a squad of players who want to work hard and put the right preparation in. The camp is very confident but we never take anyone lightly."