The Italian rocketed up the rankings last year from 45th to sixth, reaching the final of the French Open and the semi-finals in New York and winning four WTA Tour titles.
She has had another good season but has struggled over the last month on the hard courts of North America.
Maria Sharapova's withdrawal meant she was elevated to fourth seed, which for Errani was the worst thing that could have happened.
She was no match for her fellow Italian Pennetta, losing 6-3 6-1, and afterwards was distressed as she explained her troubles.
Errani said: "She played a really good match. For me it was difficult. I think the worst thing was the fight. Normally it's my best thing that I do on the court, and today was not good.
"I think it's the pressure. Everything is very difficult for me. I have never been in this situation, so it's a new situation for me. And also for my team, not only for me, my coach.
"We have to find the solution, because I think these things happen to everybody when you feel at the top and people are playing against you with no pressure and you have a lot of pressure.
"I don't want to go on the court. I don't want to go to play. I don't want to stay there on the court. I feel very bad.
"So that is the problem for me. I have to find a way to find the motivation to go there, because if I go there and I know that if I lose it's very bad and if I win it's normal, it's not a good thing. It's not the way.
"I have to find a way to stay there and fight. That is important. I hope to find it."
Pennetta, who missed last year's tournament through injury, has been a consistently good performer in New York, reaching the quarter-finals three times, including two years ago when she beat Sharapova.
There were no alarms for the top two seeds, with Serena Williams beating Galina Voskoboeva 6-3 6-0 and Victoria Azarenka almost as comprehensive in a 6-3 6-1 victory over Aleksandra Wozniak.
Williams had been due to play on Wednesday but her match was cancelled because of the rain, and she will have to come back on Friday and play her third-round match against Yaroslava Shvedova.
She is also in the women's doubles with sister Venus, but the defending champion has no worries about the scheduling.
She said: "I usually play every day. In regular tournaments I don't have a day off. Only in the grand slams I get the luxury of having a day off. I guess I didn't get that, so I'm definitely used to it."
Ana Ivanovic, seeded 13th here, also had a comfortable win, beating Alexandra Dulgheru of Romania 6-2 6-1.
Ivanovic can certainly empathise with Errani having reached world number one following her French Open victory in 2008 and then wilted under the pressure.
She has spent the last five years trying to get back to the same level, and is yet to manage it.
The Serbian said: "I think it's harder to stay there than to get there because the expectations are higher. Everyone is playing their best tennis against you and trying to beat you and to bring you down.
"There is obviously pressure from your own country, from the media, and everything else that you put on yourself, the expectations that you have from yourself. And sometimes when you don't match that, if you're a perfectionist, it can actually hurt you.
"This was probably the hardest lesson that I learned. Now, looking back, I wish I just trusted myself."
Eighth seed Angelique Kerber had a tricky draw against rising star Eugenie Bouchard, and she was given a real battle before coming through 6-4 2-6 6-3.
Ninth seed Jelena Jankovic is also through, beating Alisa Kleybanova 6-3 6-2 to end the Russian's first grand slam since she recovered from cancer.
Wimbledon finalist Sabine Lisicki, seventh seed Petra Kvitova, and former champion Svetlana Kuznetsova were other winners.
Sixth seed Caroline Wozniacki played the first match of the night session on Arthur Ashe and brushed aside Chanelle Scheepers of South Africa 6-1 6-2.
The Dane is the highest seed left in the third quarter of the draw after Errani's exit and looks in good form.
There were no more late-night heroics from 17-year-old American Victoria Duval, who lost to Daniela Hantuchova 6-2 6-3.
The qualifier produced the performance of the day on Tuesday to knock out former champion Sam Stosur but was well beaten by the Slovakian.