Ms Davidson said she had taken the decision to stand down as she wanted to concentrate her time on her young family.
But she also highlighted "the conflict I have felt over Brexit", adding: "I have attempted to chart a course for our party which recognises and respects the referendum result, while seeking to maximise opportunities and mitigate risks for key Scottish businesses and sectors."
Lord Young of Cookham, a government whip in the upper house, was more direct, saying was "very unhappy" with the Prime Minister's decision to prorogue Parliament for an extended period as the the October 31 deadline for Brexit looms.
The resignations came as Leader of the House of Commons Jacob Rees-Mogg hit back at the PM's critics, saying the outpouring of outrage it triggered was "phoney".
The leading Brexiteer also hit back at Commons Speaker John Bercow's criticism, saying it was "not constitutional" for the Speaker to intervene in such a way.
Mr Rees-Mogg insisted the prorogation move was not intended to limit the time available for MPs to debate Brexit but will allow the Government to tackle other issues.
He said: "I think the outrage is phoney and it is created by people who don't want us to leave the European Union and are trying very hard to overturn the referendum result and don't want the benefits of leaving the European Union."
He added: "Parliament wasn't going to be sitting for most of this time anyway. This is completely constitutional and proper."
On Mr Bercow's intervention, Mr Rees-Mogg said: "It is not constitutional for the Speaker to express his opinion without the direction of the House.
"He has had no such direction and therefore his comments were in a private capacity. They can't be as Mr Speaker."
Mr Rees-Mogg led the Government's defence of the prorogation as Labour and opposition parties vowed to press ahead with attempts to block a no-deal Brexit using legislation despite the decision to suspend Parliament for more than a month before the October 31 exit deadline.
Shadow international trade secretary Barry Gardiner said: "It is going to be extremely difficult. That's why the Government is disingenuous to say this is not about trying to stop us doing that.
"We will be seeking measures on Monday to try and have what is known as a Standing Order Section 24 debate. We will seek to try and put through the appropriate legislation in this constrained timetable that the Government has now put before us.
"Downing Street is lying when it claims this is about the conference recess. If he wanted to get on with his domestic agenda, he would in fact be having a shorter period of prorogation."
Thousands of people rallied for hours outside Parliament on Wednesday night, and there were smaller demonstrations in other towns and cities as Remainers reacted to the prorogation announcement.
More than one million people have also signed a petition calling on Mr Johnson not to suspend Parliament.