Chhetri, who scored five out of India's eight goals, was all praise of the other two Indian goal-getters on Saturday -- Suresh Singh and Sahal Abdul Samad.
India drew against Bangladesh and Sri Lanka in their first two matches which had put them in danger of missing the final but the win against Nepal brought them back in the reckoning.
Chhetri scored in the 62nd and 71st minutes after Manvir Singh had given India the lead in the 33rd minute in the must-win match for India.
The worst performance for seven-time champions India before this edition was the third-place finish in 2003 and the country has either won or finished runners-up in 11 previous editions.
He is now on joint third with UAE's Ali Mabkhout (77) in the list of highest scorers among active footballers, behind Cristiano Ronaldo (112) and Lionel Messi (79).
SAFF Championships: 10-man Bangladesh hold India 1-1 despite Sunil Chhetri's 76th international goal
Sunil Chhetri, playing in his 121st match for India, struck in the 27th minute to place himself just a goal shy of legendary Pele.
Despite India's 'little bit of superiority', every SAFF C'ships match is 'war to fight': Captain Sunil Chhetri
India, who have won the regional football tournament seven times out of the 12 editions, open their campaign against Bangladesh on Monday.
The five-team SAFF Championships will be held from October 3 to October 13 at the National Stadium in Male.