The Russian bomber crashed into a mountainside on Syrian soil after being hit by a missile from a Turkish jet
Writing in the UK’s Times newspaper, Mr Davutoglu stressed that fighting Islamic State was the main priority.
But he also said Turkey must protect its sovereign territory.
Russia says a Turkish F-16 fighter jet shot down one of its SU-24 bombers over Syria on Tuesday. Turkey says the bomber violated its airspace.
The plane crashed into a mountainside in a rebel-held area close to the Turkish border.
One of the two Russian pilots was killed by gunfire as he parachuted from the burning jet. The other pilot was rescued by Russian and Syrian special forces.
Tensions have sharply escalated between the Ankara and Moscow over the incident, with Russian President Vladimir Putin warning of “serious consequences”.
On Thursday, he also rejected Turkey’s claims that it did not know the downed plane was Russian.
Mr Putin was speaking after meeting his French counterpart Francois Hollande in Moscow and pledging closer co-operation against IS militants.
IS has claimed the 13 November attacks in Paris which killed 130 people, and a group’s affiliate has said it bombed a Russian passenger plane in October, killing all 224 passengers on board.
Russia has been carrying out air strikes against opponents of President Bashar al-Assad since late September.
Turkey, which is a member of a US-led coalition, insists Mr Assad must step down before any political solution to the crisis is found.
“The downing of an unidentified jet in Turkish airspace was not – and is not – an act against a specific country,” Mr Davutoglu wrote in the Times.
He pointed out that “Turkey took action, based on standing rules of engagement”, adding that “the measures to defend our territory will remain in place”.
But the prime minister also stressed that “the necessary discussions are now taking place”.
Mr Davutoglu warned that the international community “must not turn on itself”, urging a united front in fighting IS.
Turkish President Recep Tayyip Erdogan earlier rejected calls by Russia to apologise, saying Ankara did not need to say sorry for the violation of its airspace.
However, he told France 24 television: “If we had known it was a Russian plane, maybe we would have warned it differently”.
In another interview with CNN, Mr Erdogan said he was “saddened by what happened” but again refused to apologise.
On Thursday, Mr Putin insisted it was “impossible” for Turkey not to have known it was shooting at a Russian plane.
“We had informed our American colleagues in advance about where, when and on which echelons our pilots will work.” he said.
“The American side, which heads the coalition in which Turkey takes part, knew about the time and the place where our planes were,” he added.
The Turkish military says it sent a number of warnings to the Russian jet before firing a missile, some 17 seconds after the plane entered Turkish air space.
The surviving Russian pilot has said he received no such warning and was adamant the plane did not stray out of Syrian air space.
Russian PM Dmitry Medvedev has warned after the incident that food products, Turkish interests in Russia and a number of joint investment projects could be affected.
Turkey and Russia have important economic links. Russia is Turkey’s second-largest trading partner, while Turkey is one of the biggest foreign destinations for Russian tourists.