Yasuhito Endo put the Blue Samurai in front in the 14th minute at a sellout Sapporo Dome, sweeping home after a dazzling run down the right from Yuichi Komano.
Spain-based striker Miku pegged Japan back, twisting while on the ground to deftly poke the loose ball past goalkeeper Eiji Kawashima with the outside of his right boot.
"First half, (we) got early goal but should have capitalised on that, taken more chances," Japan coach Alberto Zaccheroni told reporters.
"In the second half we created a few chances but I thought our pace dropped off a bit."
Keisuke Honda, sporting a new-look blond mohican haircut, could have put Japan 2-0 up well before the half-time whistle, only for his left-foot drive to thump off the post.
Kagawa also contrived to miss an open goal in the 75th minute, his shot looping up against the crossbar with the goal at his mercy.
"We were at home and had lots of chances to score so I feel deeply sorry we didn't manage to win," said Kagawa. "It's really disappointing. We'll put it right for the World Cup qualifiers."
Honda praised Venezuela, who finished fourth at last year's Copa America.
"They're a tough side," said a bare-chested Honda. "They put us under a lot of pressure and didn't let us play our game. We will have to increase our work rate."
Japan meet United Arab Emirates early next month in their final tune-up for a World Cup qualifier against Iraq on Sept. 11.
They overpowered Oman 3-0 and Jordan 6-0 at home before being held 1-1 in Australia in June in their first three games in the final round of Asian 2014 World Cup qualifiers.