Former Pakistani skipper Imran Khan and his Indian counterpart Sunil Gavaskar said Malik needed to prove he deserved a place in the side as a batsman after the tourists' six-wicket loss here.
Both, however, lauded India's veteran leg-spinner Anil Kumble, who led his team to victory in his first Test as captain.
"Malik is a captain who is not in control at the moment and that will not change till he proves that his position in the side as a batsman is undisputed," Khan wrote in his column in the Hindustan Times newspaper.
Malik flopped in both innings at the Ferozeshah Kotla ground, scoring nought and 11.
"Malik has the potential to be a good captain because he has a calming presence on the field and is a good fielder to boot," said Khan.
"However, if his own form does not improve, he will be unable to show any flair in his leadership role. He will remain tentative, and his risk-taking abilities will be found wanting."
Malik has so far captained the team in only three Tests since taking over the role from Inzamam-ul-Haq this year. He has already lost a two-Test series, against South Africa at home last month.
"This Pakistani team is still searching for an identity, especially after the retirement of Inzamam, who was not only an inspirational skipper but also like a benign elder brother to all," Gavaskar wrote in the Times of India.
"Malik does not quite have the same personality nor the standing among his teammates to be able to get the response that Inzy did.
"He comes across as a mild-mannered individual, who because of his own place in the team not being certain, will not crack the whip."
In contrast, 37-year-old Kumble impressed both as a captain and a bowler. He was named man of the match for taking seven wickets.
"Kumble is not only a giant in Indian cricket, but whose attitude towards it is a no-nonsense one, and so, there won't be any tomfoolery on the field while he is in charge," said Gavaskar.
"He picked up wickets in both innings. He also made the right bowling changes and looked in charge from the word 'go'."
Kumble replaced as captain Rahul Dravid, who quit following his team's Test series victory in England in September.
"Ironically, it was India who was playing under a new captain, but since the 'debutant' in question had 17 years of experience behind him, he looked the part," said Khan.
"Kumble has the stature to command respect of his team, and since he is a bowler, was good with his bowling changes. He led by example and was tenacious even when things were not going his way."
The second match of the three-Test series starts in Kolkata on Friday.