Osaka's last match before arriving at the All England Club was a comfortable defeat by Putintseva at the Nature Valley Classic in Birmingham and again the Kazakh proved too consistent.
Osaka led by an early break but could not hold onto her advantage and Putintseva celebrated a 7-6 (4) 6-2 victory and one of the biggest successes of her career.
It was clear how disappointed Osaka was by the defeat in her press conference as she spoke barely louder than a whisper and gave very brief answers.
The 21-year-old has not reached the final of any tournament since winning her second successive grand-slam title at the Australian Open in January and climbing to world number one.
Handling the extra attention and pressure has been a big challenge and, asked how she has picked herself up in the past, Osaka said: "The key for me was just having fun, I guess, kind of taking pressure off myself. I hope I can somehow find a way to do that."
After contemplating answering the next question about how difficult it has been to adjust to her new level of fame, Osaka turned to the moderator and said: "Can I leave? I feel like I'm about to cry," before walking out.
There was also a first-round loss for 16th seed and French Open finalist Marketa Vondrousova, who struggled with a hand injury during a 6-4 6-4 loss to American Madison Brengle.
Tenth seed Aryna Sabalenka, meanwhile, continued to struggle after her breakthrough 2018, losing 6-2 6-4 to 2017 semi-finalist Magdalena Rybarikova.
Third seed Karolina Pliskova had to save three set points in the second against China's Zhu Lin before coming through 6-2 7-6 (4).
Pliskova is among the big favourites to win the title and arrived at the All England Club having blitzed the field to lift the trophy at Eastbourne on Saturday.
But she was not at her best against Zhu, who has never won a grand-slam match, and the Chinese player held set point three times serving at 6-5. Pliskova managed to break, though, and came out on top in the tie-break.
The Czech, who has only once made it past the second round here, said: "It's tough to compare with the week in Eastbourne. I think it was quite normal. Of course, it went a little bit longer, and I almost dropped a set. It's still almost. I played two sets, that's fine.
"I think my timing was a little bit off today. I just didn't have any chance to hit on the match courts, which I felt were totally different than Aorangi (practice) courts."
Seventh seed Simona Halep was given a tough battle by Belarusian Aliaksandra Sasnovich before battling to a 6-4 7-5 victory.
Halep, who has made the quarter-finals twice and the semi-finals once, trailed 5-2 in the second set and had to save a set point at 5-4 before sealing victory with a run of five games in a row.
Halep suffered a nasty-looking slip during the first set and called for the trainer prior to the start of the second.
The Romanian said: "It's OK in this moment. But I need to do the treatment. I feel it a little bit. I think it's a little bit stretched, the muscle behind the knee, and also the Achilles. Hopefully it's nothing dangerous and I can recover until the next match."
Eighth seed Elina Svitolina was a 7-5 6-0 winner over Daria Gavrilova but last year's junior champion, Pole Iga Swiatek, was beaten by Viktorija Golubic.