Beijing has accused Lee of using his visit to push for Taiwan's independence.
Lee defended his visit as a "private event", but his comments come a few days after Costa Rica cut diplomatic ties with Taiwan in favour of China.
On Wednesday, Oscar Arias, the Costa Rican president, announced the Central American country was cutting ties with Taiwan as it needed to strengthen ties with China in order to attract foreign investment.
Beijing welcomed the move, saying it opened the way to "beneficial cooperation" with Costa Rica.
Lee also accused Beijing of overreacting to his visit to Yasukuni shrine, Japan's controversial temple to its war dead, saying Beijing was using the issue to divert attention from problems at home.
"The Yasukuni problem was invented by the Chinese and Koreans because they could not deal with problems in their own country"
former Taiwanese president
Taiwan is a former Japanese colony and Lee's elder brother, who was killed in 1945 while serving with Japan's navy during the Second World War, is listed among the 2.5 million war dead honored at Yasukuni.
"I see no problem with countries honoring young soldiers who gave their lives for their country," he said.
"That is not something that foreign governments should criticise."
Lee said that the "Yasukuni problem was invented by the Chinese and Koreans because they could not deal with problems in their own country".
China strongly objects to public figures visiting the site, which enshrines a number of war criminals, and views such visits as a glorification of Japan's military past.
Consequently Yasukuni has been a frequent flash point between Japan and China.