"We do not know why India showed its desperation and allowed the country to be equated with Pakistan on the issue of NSG membership," party's senior spokesman Anand Sharma said
"It's high time that Prime Minister Narendra Modi realises that diplomacy requires gravitas, depth and seriousness. PM Modi needs to realise diplomacy needs depth not public tamasha," he said.
"The world saw the PM make a spectacle of himself and India. Now India faces embarrassment unnecessarily," Sharma told reporters.
He said the intense lobbying by Modi government was "unnecessary".
Sharma said, "This kind of intense lobbying Prime Minister Modi and his government, we can understand should have done for the UN Security Council membership. When there is no obstacle when it comes to nuclear trade within the NSG countries, it was unnecessary."
The plenary meeting of the 48-member NSG ended on Friday without any decision on India's membership bid as divisions persisted over admitting non-NPT members with China leading the opposition to it.
Ahead of the meeting, India had pushed its case with a number of countries, with Prime Minister Narendra Modi leading the charge.
Modi had also met Chinese President Xi Jinping in Tashkent urging him to take a decision on India's membership on merit while seeking Beijing's support but China persistently opposed India's bid.
Is India prepared for Brexit?
PHOTOS: How Twitter reacted to Brexit
'Independence Day': Britain parts ways with EU
Shock, bewilderment, awe: Britain reacts to Brexit
After Brexit, what next?