* Ford of Canada, Unifor union say deal has drawbacks
* S. Korea has little appetite for Canadian vehicles
* Canada needs more trade pacts to compete, analysts say
* Auto sector employed 117,200 in Canada last year
TORONTO, March 11 (Reuters) - A new free trade agreement with South Korea will throw a wrench into Canada's auto sector recovery, union leaders and an automaker warned on Tuesday, highlighting the pressure on an industry already struggling with competition from Mexico.
The pact, which immediately drew fire from Ford Motor Co of Canada Ltd and Canada's largest private-sector union, underscores problems with the size and cost of cars being produced in the country's industrial heartland, experts said.
"We don't, in Canada, build the type of vehicles that are much in demand in South Korea," said Tony Faria, a University of Windsor professor and auto industry expert. "It's not as if any trade deal we set up with South Korea is necessarily going to result in more vehicles being exported."
Canada and South Korea said earlier on Tuesday they had wrapped up talks on a long-delayed free trade deal, Canada's first in fast-growing Asia. Canada's Conservative government touted the benefits of the deal, which is expected to boost farm product exports.
But Unifor, a union representing more than 39,000 workers in the country's auto sector, estimates that 33,000 manufacturing jobs in Canada could be lost from the pact, including up to 4,000 auto assembly and parts jobs.
"I wouldn't say it's the death of the industry, but it's another nail (in the coffin)," said Jerry Dias, Unifor's national president.
In 2013, the auto sector employed 117,200 people in Canada, according to Statistics Canada. Some 96,700 of those jobs, or nearly 83 percent, were in Ontario, the most populous province.
Ford Canada Chief Executive Dianne Craig was equally harsh.
"No Canadian manufacturer can compete with a market controlled by non-tariff barriers and currency manipulation. The trade agreement negotiated by the Canadian government with South Korea fails to address these issues," she said in a statement.
Canadian Prime Minister Stephen Harper said that Ford was being hypocritical given its support for the U.S.-Korea free trade deal.
Ontario's government was disappointed that the 6.1 percent tariff on South Korean auto imports will be phased out in three annual cuts and not a longer period. South Korea's 9 percent tariff on imports will be eliminated immediately.
Ontario's Minister of Economic Development, Trade and Employment, Eric Hoskins, said he was also unhappy that Canada was unable to negotiate the same "snap-back provision" included in the U.S.-Korea deal. Such snap-backs would roll back tariff reductions if it was shown that Korea used non-tariff barriers to protect its market.
Canadians bought more new vehicles in 2013 than ever before, as consumers brushed off high debt to buy more trucks and luxury vehicles. Sales jumped 4 percent, topping the previous record-setting year in 2002.
Still, Canada's auto industry has seen a slow, long-term decline, in terms of its share of North American auto production and investment.
Since the North American Free Trade Agreement was signed 20 years ago, auto production in Mexico has more than tripled, while production in Canada has only edged higher, Scotiabank senior economist Carlos Gomes said in a report.
"Your problem is Mexico at this point, it really, really is," said Sean McAlinden, chief economist of the Center for Automotive Research, who pointed to a surge of production plant investment in the low-cost jurisdiction.
Within two years, Mexico will likely produce two cars for every vehicle assembled in Canada, he said.
"To offset the Mexican advantage ... Canada needs more free trade agreements to sell vehicles worldwide. Period. You just can't rely on the Canadian or even the North American market," McAlinden said.
But there appears to be little appetite in South Korea for the large vehicles assembled in Canada, including vans, sedans and sport-utility vehicles.
Ford Canada said that Canadian vehicle and parts exports to South Korea totaled C$15 million in 2013, while similar imports from that country added up to C$2.8 billion.
MIXED INDUSTRY RESPONSE TO DEAL
Not all automakers with production in Canada were opposed to the trade deal.
The Japanese Automobile Manufacturers Association of Canada, a group that includes Toyota Motor Manufacturing Canada Inc and is chaired by Honda Canada Chief Executive Jerry Chenkin, endorses the agreement because it could pave the way for a similar pact with Japan.
"We urge the government to rev-up trade negotiations with Japan and the 12 countries in the Trans Pacific Partnership," said the group.
General Motors Co, whose GM Korea Co subsidiary is that country's third-largest automaker, said in 2010 that it supported the U.S.-Korean free trade deal. Hyundai Motor Co and its smaller subsidiary, Kia Motors Corp , dominate the Korean market.
"We will continue to work closely with the Canadian and Korean governments to ensure the agreement is implemented in a way that brings the full benefit of fair competition to customers in both markets," GM Canada said in a statement.
Chrysler Canada, a unit of Fiat Chrysler Automobiles , declined comment. Fiat Chief Executive Sergio Marchionne said last month that he dropped his opposition to the deal after Canadian Prime Minister Harper reminded him that his company did not reject the U.S. trade deal with South Korea.