Inexperienced Zimbabwe fast bowler Tendai Chatara took five for 61 as Pakistan were bowled out for 239 despite an unbeaten 79 by Pakistan captain Misbah-ul-Haq.
"The batting is a bit of a worry," said Misbah, looking ahead to Pakistan's next Test series, against world champions South Africa in the United Arab Emirates next month.
"All the batsmen have to learn from their mistakes. You can't win Test matches with twenties and thirties. You have to score big runs like Younis Khan did in the first Test."
Misbah and opening batsman Khurram Manzoor both scored two half-centuries in the second Test, while Younis contributed 77 in the first innings. But the rest of the batting failed against the spirited Zimbabwean attack.
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"Zimbabwe deserved the victory," said Misbah. "They played excellent cricket in the first Test as well. From the start they were positive and they kept us under pressure throughout the game."
Zimbabwe captain Brendan Taylor praised his team. "It takes a lot of character to come back from a big loss. Beating a world-class team is a wonderful feeling."
Taylor said Zimbabwe's performance in the first Test, in which they were on top for much of the match, had shown the importance of not relaxing. "Even though we won the Test we learnt a lot from the way Pakistan went about playing.