"But this is a very different situation."
Joyce said he wanted English to stay on as leader, and his intention was to stick around as well.
"It has been an interesting 24 hours. But as Bill said last night, that's the way MMP works. That's the way democracy works. And we wish the new Government all the best."
Judith Collins, who would be a possible leadership contender, told Breakfast that English did a fantastic job during the campaign.
"I don't see any sense of change at the moment," Collins said. "I am very much looking forward to being part of a very strong opposition led by Bill English.
"I think he has a huge mandate from the caucus. We are very united. I am just so looking forward to holding the next Government to account. It's going to be an interesting time."
Brett Hudson was one of several National MPs to watch English address media at the Beehive last night. He said English had run an excellent campaign.
"Bill did an absolutely fantastic job. You look at the numbers... Bill can be phenomenally proud.
"I think we are all going to take some time to adjust to a role in opposition. Bill has my confidence. I believe he has the confidence of my colleagues... the decision should be his. And I don't think it is a decision that anyone should be rushed into."
Another senior National figure told the Herald it would be English's call on the leadership.
"I think he would be genuinely appalled that having got that sort of result that he is not the Prime Minister.
"It has only been a day. I don't sense any moves on him. I think he's pretty much there - if he wants to be there, he's there."