Sources have reported that some Conservative ministers have attempted to dissuade Mr Gove from his leadership bid so that the party can unite around presumed frontrunner Theresa May.
Within couple of hours after Gove entered the fray, Johnson announced his withdrawal saying he had too little support among MPs to stand for the leadership.
"I've taken some hard decisions, but I've always taken those because I've put my country and my principles first", he told BBC One's Andrew Marr Show.
Gove, who is running to replace David Cameron as Britain's prime minister and Conservative leader, says he is committed to taking Britain out of the EU.
Cameron, who campaigned hard for Britain to stay in the European Union, has said he will leave it to his successor to start formal exit talks.
Asked about Mr Johnson's decision to exit the race, Ms Davidson said yesterday: "It's not for everyone".
The two front-runners are Minister of Interior Theresa May, who is considered a consensual candidate, and former Mayor of London Boris Johnson.
Mr Gove said he accepted that "all sorts of people would attack me personally" as a result of his decision, which has been widely viewed as an act of betrayal and may have fatally damaged his chances of winning the leadership contest.
Mr Johnson's shock decision not to stand catapulted Mrs May into pole position, with Mr Gove positioning himself as the leading Brexiteer in a field of five contenders also including Work and Pensions Secretary Stephen Crabb, energy minister Andrea Leadsom and former defence secretary Liam Fox.
His comments are likely to upset and annoy European Union leaders, who have put strong pressure on Britain to start talks soon on leaving the 28-nation bloc.
He said that, while he had "enjoyed" working with Johnson during the referendum campaign, the former mayor - who has often been labelled as "bumbling" - lacked "grit, executive authority, sense of objective, clarity".
The UK needed a leader who both believed in a new path and who could build and lead a united team to guide through the challenges ahead, Gove said.
"We will continue to be tough on the deficit but we must be realistic about achieving a surplus by the end of this decade", Osborne said.
The ex-mayor was also berated by a member of the public who said he was an "absolute disgrace" and had run away from his responsibilities after helping to secure a Brexit vote. What is the right thing to do?
Two south Lincolnshire MPs who were on opposite sides of the EU (European Union) referendum argument are united together at the start of the Conservative Party leadership contest.
Asked if May could row back from the Brexit vote, Simon Usherwood, senior fellow at the United Kingdom in a Changing Europe think tank, said: "Realistically, no".
But Gove said "I have no expectation that Article 50 would be triggered in this calendar year".
But Mr Gove said putting friendship first in politics did not serve the country.