“The tour is not over,” said Kohli ahead of a three-match Twenty20 series starting at the Wanderers Stadium in Johannesburg on Sunday.
After leading India to a crushing 5-1 one-day international series victory to compensate for a 2-1 Test series defeat to the South Africans, Kohli said India were still hungry for success.
“That is the frame of mind we are in and we are looking forward to the T20s now,” he said.
Kohli capped an exceptional personal performance by hitting 129 not out in the sixth one-day international in Centurion on Friday, taking his aggregate to a world bilateral one-day series record of 558 runs at an average of 186.
Shastri lauded Kohli's leadership and his batting skills: “I've seen him batting across all conditions, all formats. It's not just averages, it's the way you get runs, when you get it and then to back those runs up on what the team does.
"I would safely say he is the best batsman in the world.”
'No backward steps'
Asked whether he considered himself the best, Kohli told journalists: “I am not competing with anyone. I only look to help my team. If you are thinking about the team special things happen. If you are thinking about being ahead of someone else, you'll be found out very soon by this game.”
Kohli said India had pledged not to take “a backward step” after losing the first two Tests in South Africa.
He said their win in the third and final Test had been a turning point.
“We have created momentum which has lasted until now. It's with us and we have to make the most of it, even until the last day of the tour.”
Ten of the 13 Indian players who appeared in the one-day series are in the T20 squad, while eight of South Africa's squad played in the one-day games.
With a Test series against Australia starting on March 1, South Africa have rested all their likely Test players with the exception of AB de Villiers.
De Villiers, who was once himself described by Kohli as the best batsman in the world, had a poor one-day series in comparison to his Indian Premier League teammate, making only 62 runs in three innings and needs to find his best form ahead of the Tests against Australia.
A key for South Africa will be to master Indian wrist spinners Kuldeep Yadav and Yuzvendra Chahal, who took a combined 33 wickets in the one-day games.
South Africa: JP Duminy (captain), Farhaan Behardien, Junior Dala, AB de Villiers, Reeza Hendricks, Christiaan Jonker, Heinrich Klaasen (wkt), David Miller, Chris Morris, Dane Paterson, Aaron Phangiso, Andile Phehlukwayo, Tabraiz Shamsi, Jon-Jon Smuts
India: Virat Kohli (captain), Rohit Sharma (vice-captain), Jasprit Bumrah, Yuzvendra Chahal, Shikhar Dhawan, MS Dhoni (wkt), Dinesh Karthik (wkt), Kuldeep Yadav, Bhuvneshwar Kumar, Manish Pandey, Hardik Pandya, Axar Patel, Lokesh Rahul, Suresh Raina, Shardul Thakur, Jaydev Unadkat
March 18, Johannesburg
March 21, Centurion
March 24, Cape Town