The 30-year-old striker, who has joined the Cobblers from Leeds on a free transfer, said: "I don't feel 30. I'm not worried about my age at all.
"A lot of people still think I'm 24 or 25," he told BBC Radio Northampton. "So I suppose that tells you I don't move like a 30-year-old."
Constantine had a year left on his deal at Leeds but was keen on a fresh start.
The big striker, signed from Port Vale only last August, had a luckless time of it at Elland Road, picking up several injuries, the worst of which was a broken arm suffered after scoring a goal on New Year's Day.
That proved to be his only strike in 11 frustrating months at Leeds. But the much-travelled striker has scored goals with relative consistency at other clubs he has been at, most notably at Southend and Port Vale, for whom he hit 26 in his final campaign two seasons ago.
And he is hoping that being at a new club will kick-start his career again.
"It's not that it didn't work for me," said. "It's just injuries.
"The fans loved me there but this is a new chapter for me now."
BBC