"Not one single Scottish MP was able to speak in a debate that lasted less than 20 minutes", he said.
Mr Blackford said Scotland had been "plunged into a constitutional crisis" as a result of the UK Government's actions and demanded that emergency legislation be brought forward.
May responded by denying it was a powergrab, saying the Scottish Parliament will get legislation over 80 new areas.
Mr Lewis said: "It was quite a dramatic PMQs and it seems like she stole the show after the SNP because the Speaker called her out basically and said what a well-behaved baby".
The SNP can not stand by while Scotland's voice is silenced, while our Parliament is undermined and our devolution settlement - which Scotland overwhelmingly voted for - is put at risk.
And lodging his protest Mr Blackford blasted: 'This is a power grab and MPs from Scotland were not even given the courtesy of debating it last night. Yet the United Kingdom government proceeded to downgrade devolution and defy the Scottish people.
After Mr Blackford refused to sit down, Mr Bercow eventually banned Mr Blackford from the Commons for the rest of the day - prompting all SNP MPs to walk out.
"I'm not hearing that at this time and it is my clear understanding that I'm not obliged to do so", said the speaker.
We could have the vote now or it could be taken at the end...
"I've just been advised that the father is the Honourable Gentleman the Member for Norwich South - I'm not going to go so far as to say his behaviour is always impeccable, but the little baby has been impeccable and I think we salute that". My mixed sequence of advice is that is better for the vote to be conducted at the conclusion of questions to the prime minister...
"That is not acceptable and the Speaker refused to allow a division which I rightly called for".
Mr Blackford said it was a "democratic outrage" that more time had not been allocated to debating the issue on Tuesday and said he had "no option but to insist that this house sits in private".
All of the SNP's 35 MPs then stood up and walked out collectively.
In the central lobby immediately afterwards, Blackford told the BBC he would not back down.
The Sewel Convention says that the United Kingdom government can not legislate without the consent of the Scottish Parliament on devolved matters - consent was denied and yet the Tories railroaded through their power-grab.
He added the issue would "haunt the Scottish Tories for a generation".