"The plane disappeared and then reappeared in Syrian airspace, flying at 100 metres altitude and about 1-2 km (0.6-1.2 miles) from the Syrian coast," he told a news conference about the incident on Friday.
"We had to react immediately. Even if the plane was Syrian we would have shot it down," he added.
Makdissi said the jet -- a Turkish air force F4 Phantom -- was downed by anti-aircraft fire, not by a radar-guided missile. "The bullets only have a range of 2.5 km (1.5 miles)."
Turkey summoned a NATO meeting for Tuesday to consult its allies and agree on a response to what it says was an attack without warning in international airspace.
He was unclear on how the episode might affect relations with its once friendly neighbour, which turned against President Bashar al-Assad last year as violence in Syria increased and thousands of refugees fled to safety in southern Turkey.
"What was said by the Turkish (government) is different from reality ... They have complicated the situation," Makdissi said.
Despite the incident Syria remains committed to a "neighbourly relationship" with Turkey, he said. "We live in a tense situation with Turkey, but we don't have hostile intentions towards the Turkish people."
The Phantom's two crewmen are missing. The wreckage of their plane is lying in deep water off the Mediterranean coast.
A "coordinated" Syrian-Turkish search-and-rescue operation to find the two crewmen was continuing, he said, adding that some of the wreckage had been found and turned over to Turkey.
Makdissi ended with a warning against any action by the NATO military alliance, which helped Libyan rebels overthrow dictator Muammar Gaddafi last year.
"NATO is supposed to be there to strengthen countries," he said. "If their meeting is for hostile reasons (they should know that) Syrian land and waters are sacred."
A Syrian general and 38 other soldiers defected to Turkey overnight, state television said on Monday, escalating tensions between the two neighbours.