New Zealander Vern Cotter coached the Scots to wins over Argentina and Tonga last November before a disappointing Six Nations campaign in which they lost all five matches, though mostly by small margins.
"Scotland have got some very good players now and have shown that they can compete against the top sides in the world," Southwell told Reuters.
"We have forwards who can guarantee quality ball and an exciting back line capable of scoring tries but we have to be more ruthless against the best teams."
Scotland gave England a real scare at Twickenham in this year's Six Nations, leading 13-10 at halftime after producing some fine attacking rugby.
They were over-run in the second half, however, losing 25-13 and a home defeat by Italy left them bottom of the standings.
"The loss to Italy will have hurt the players but they should be encouraged by a lot of things they did in the tournament," Southwell said.
"Vern Cotter has changed the way they play and changed the players' mindset.
"If they can learn from the mistakes Scotland can reach the World Cup quarter-finals which should be their minimum target."
Scotland are in Pool B with South Africa, Samoa, the United States and Japan.
They start their campaign with a must-win game against the Japanese on Sept. 23 before facing the United States, South Africa and finally Samoa, in a match that could decide which team makes the last eight.
"Scotland should beat Japan but the Americans will be difficult opponents," Southwell said.
"Nobody would expect Scotland to beat South Africa but that game will be good preparation for Samoa who will be very physical opponents."
Scotland's traditional strength has been in a well-drilled and powerful forward pack but Southwell believes their backs have the talent to shine on the world stage.
"Stuart Hogg has shown he has the pace and skills to be one of the most exciting fullbacks in the world," Southwell said.
"(Scrumhalf) Greig Laidlaw is a captain who leads by example and he knows how to get the team round the pitch.
"If the forwards can get enough quick ball Scotland have the firepower to cause problems for anyone."
Scotland's best World Cup performance was their fourth place finish in 1991. They failed to reach the quarter-finals for the first time in the 2011 tournament in New Zealand.
(Editing by John Mehaffey)
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