The MP still considered the motion a success, saying a strong message had been sent to the prime minister that things needed to change.
"Now it's right that we give him the opportunity to implement the changes," Mr Simpkins told ABC radio.
Senator Chris Back agreed the motion was a "wake-up call" for the leadership team to consult widely.
"Nobody can make the assumption that from the numbers ... the spill gave any indication at all as to how people might have voted had the spill motion passed," he told Fairfax radio.
The Western Australia senator said it was a backbench motion, not a Malcolm Turnbull-led conspiracy.
"He was not out there canvassing, he was not the catalyst for this," he said.
Senator Dean Smith, who backed the prime minister, agreed that Mr Turnbull was a team player and did not think anyone could accuse him of any wrongdoing.
He also agreed that Mr Abbott deserved time to improve his performance, saying the leader had listened to members' concerns.
"I'm confident that the message has been heard and he will focus now on the things that are really important to Australians and that is first and foremost the economy," he said.
- AAP