Earlier, China made the fresh pitch to raise the Kashmir issue under "other matters" during closed consultations in the Security Council Consultations Room.
"We once again saw an effort made by one member state of the UN, fail in plain view of all others," India's Permanent Representative to the UN Syed Akbaruddin said.
"We are happy that neither alarmist scenario painted by the representatives of Pakistan nor any of the baseless allegations made repeatedly by representatives of Pakistan in the UN fora were found to be credible today," Akbaruddin told PTI.
"We are glad that the effort was viewed as a distraction and it was pointed by many friends that bilateral mechanisms are available to raise and address issues that Pakistan may have in its ties with India," he said.
A European source, heading into the UNSC meeting, described the discussions on Kashmir during the closed consultations to be "low key."
A top European diplomat said the issue should be resolved bilaterally and it was a "domestic affair".
Akbaruddin further said, "Pakistan's practice of using false pretences to distract from addressing the malaise that afflicts it has run its course. We hope that Pakistan pays heed to the clear signals sent out here today and focusses on the hard tasks it has to address in order to ensure normal relations with India."
Coming out of the meeting, Chinese Ambassador Zhang Jun said: "We had a meeting on Jammu and Kashmir.
And I'm sure you all know that Foreign Minister of Pakistan wrote letters to the Security Council asking it to pay attention to the current situation in Jammu and Kashmir.
"The issue of India and Pakistan has always been on the agenda of the Security Council and today we have also seen some tensions, so the Security Council had a briefing and (it) heard at the briefing from the Secretariat concerning the current situation on the ground. Members exchanged views on that."
Zhang later said China has stated its "position very clearly. We remain concerned about the situation on the ground (in Kashmir)."
When asked if the meeting advanced anything, he said: "I am sure the meeting will help both the parties to understand the risk of further escalation and will encourage them to approach each other and have a dialogue and seek solutions through dialogue. I think that will be helpful."
The current move by China was the third such attempt to raise the Kashmir issue at the UNSC since August last when the special status granted to Jammu and Kashmir
under Article 370 of the Constitution was scrapped by the government, and the state was bifurcated into two union territories.
In August, China pushed for a UNSC meeting on Kashmir. However, the meeting did not yield desired results for China as the member-states maintained that India's move was an internal issue.
Last month, France, the US, the UK and Russia foiled an attempt by China to discuss Kashmir at a closed-door meeting of the UNSC.
China has criticised New Delhi for making Ladakh a union territory. China lays claim over several parts of Ladakh.
Meanwhile, Pakistan's Prime Minister Imran Khan on Thursday welcomed the UNSC meeting on Kashmir and claimed that the issue was an internationally recognised dispute that remains on the agenda of the international body.
"An internationally recognised dispute, Jammu and Kashmir remains on the Security Council's agenda and its consideration by the Council reflects a recognition of the seriousness of the prevailing situation," Khan said.
He said the issue "must be resolved in accordance with relevant UN Security Council resolutions and the will of the Kashmiri people".
"We will continue to provide moral, political and diplomatic support to the Kashmiri people until they secure their inalienable right to self-determination," he added.
Pakistan's Foreign Minister Shah Mahmood Qureshi claimed that the UN has confirmed during its meeting on Kashmir that India's action of scrapping Jammu and Kashmir's special status has increased tension in the region.
Interacting with media persons in New York, Qureshi said at the request of Pakistan and with the support of China, the Security Council considered the situation in Jammu and Kashmir, according to a statement released by the Foreign Office in Islamabad.
"In the closed meeting of the Council, representatives of the UN and the UNMOGIP briefed the participants. The UN in its briefing confirmed that India's August 5 measures resulted in the rise of tensions and that the 'local situation' remains tense," Qureshi said.
India maintains that the UN Military Observer Group in India and Pakistan (UNMOGIP), established in January 1949, has outlived its utility and is irrelevant after the Simla Agreement and the consequent establishment of the Line of Control.
The UNSC is "monitoring the situation", said Qureshi, who is on a three-day visit to the US as part of Pakistan's efforts to defuse the tensions between the US and Iran.