Tamada halted Japan's run of two successive goalless draws when he slid the ball home from a tight angle four minutes before half-time in rain-lashed Tokyo.
Booed from the pitch after scraping a 0-0 draw with China in their opening game, World Cup-bound Japan doubled their lead when defender Tulio headed home in the 65th minute.
Tamada bundled home Japan's third with seven minutes remaining to put the home side level with the Chinese on four points and on goal difference after two matches.
"We wanted to scored a couple more goals so it's a slightly disappointing result," Okada said in a pitch-side interview while being jeered by a small section of fans among a crowd of 16,000.
"The plan was to set the tempo and play our style of football. We lost the way a bit in the second half. We will sit down and analyse the game tomorrow."
Japan realistically have to beat holders South Korea on Sunday to have a chance of capturing their first East Asian title with China facing Hong Kong in their final game.
"We won't do anything special for Korea," insisted Okada. "We'll try to do our jobs effectively and be more direct in the final third."
No host nation has won the East Asian championship since it was launched in 2003.
"We'll be doing everything we can to break that jinx," said Okada. "We are only thinking of beating Korea."
South Korea, another of the four Asian teams competing at this year's World Cup in South Africa, overwhelmed Hong Kong 5-0 before suffering a shock 3-0 defeat by China on Wednesday.
