The English champions fell behind after only a minute but they recovered to lead 2-1 heading into the second half thanks to Jesse Lindgard’s strike and a Yokohama own goal.
However, Fabio Aguiar headed the scores level before Yoshihito Fujita’s winner three minutes from time removed further gloss from United’s pre-season Asian tour.
“We had a chance to finish off the game at 2-1 and had a great chance to make it 3-1, and we thought we had chances after that as well but we didn’t take them. So it was a tough game,” said Moyes.
“It was the first time that I got a chance to see Shinji (Kagawa) playing. He had a great chance to score, but overall I was pleased to get him,” added the Scot.
Moyes also admitted United had “a couple of wee worries” over strikers Robin van Persie, who was withdrawn with a minor thigh problem, and Danny Welbeck, who had a groin twinge.
But he said unsettled striker Wayne Rooney, whose departure from the tour with a hamstring injury heightened speculation over his future, was recovering — and that he would not be leaving the club.
“So far as I know, he is coming back, he is jogging,” Moyes said. “We are not going to lose him.”
So far under Moyes, United have lost 1-0 in Bangkok and won 5-1 in Melbourne, and they got off to a horror start in hot and humid conditions in Yokohama.
The game was just a minute old when Brazilian striker Marquinhos latched on to a poor clearance from United custodian David de Gea to fire the hosts in front from inside the box.
The setback stung the Premier League champions and talented Belgian teenager Adnan Januzaj nearly put them level with a crisp strike which was just off-target.
Januzaj, 18, then got back to head a chance off the line but it was new signing Wilfried Zaha who orchestrated United’s opener when he drifted past his man into the box.
The ex-Crystal Palace man’s low cross caused mayhem and it was Lindgard on hand to net his third goal in two games, after Saturday’s brace against the A-League All-Stars.
Yokohama handed United the lead when Januzaj, United’s reserve team player of last season, fired a free-kick which came off the unfortunate Masakazu Tashiro and over the line.
But the hosts were back on terms after the break when de Gea failed to deal with a corner and Brazilian defender Fabio Aguiar’s header moved the score to 2-2.
Kagawa drew a huge cheer when he came on just after the hour-mark, and United’s Japanese playmaker nearly raised the roof when he got clear — but his shot failed to beat the ‘keeper.
Ashley Young hit one into the side-netting but it was Yokohama who had the final word when Fujita swept home the winning goal in the 87th minute.
Moyes, facing the stiff challenge of following Alex Ferguson’s 27-year, trophy-laden reign, now leads his team west for a game against Japan’s Cerezo Osaka on Friday.