Wright acts as Defoe's personal coach and gave the England striker a peptalk before kickoff.
Defoe, who had been struggling with a groin injury, revealed to The Sun: "I spoke to Ian before the game and he said 'you are due a hat-trick'.
"He texted me afterwards and said 'I love you JD, well done!' It is brilliant, as we always speak about goals.
"It's difficult to find the words to describe the feeling you get when you score a hat-trick for your country.
"To score one is fantastic, so to get a hat-trick in front of all the fans and my family - it's a special night. It's the sweetest hat-trick of my career, yes."
Defoe, who has scored 15 goals in 44 internationals, had been due to have a groin op this week but the problem has eased.
He said: "I thought I'd miss out with the injury, but I've worked really hard in the gym and now I feel good."