Kotoko secured their first three points of the campaign last Sunday when they defeated Heart of Lions, ending their winless start to the season.
Following the victory, Tinkler stressed the importance of making home advantage count, with the South African coach calling on the club's passionate supporters to play their part in creating a difficult environment for visiting teams.
"We need to make our stadium a fortress, and we need to make it very difficult for teams to come here, and the fans play a big part in that," Tinkler was quoted by Ghanasoccernet.com.
The former Orlando Pirates coach believes Kotoko must establish an intimidating atmosphere at Baba Yara Stadium, with opponents expected to feel the pressure from the moment they arrive in Kumasi.
"Teams should fear to come here because of the support base that we have and, with them, we can obviously change that history," he added.
The Asante Kotoko coach will now prepare his side for a challenging away fixture as Kotoko travel to face FC Samartex at the Nsenkyire Sports Arena on Sunday.
Ghana captain Gideon Mensah believes the Black Stars must develop greater urgency and understanding of what it means to represent the national team after their disappointing defeat to Gambia.
Eric Tinkler is reportedly set to make a return to the Premier Soccer League with the former Orlando Pirates coach having arrived in KwaZulu-Natal to take charge of Durban City.
In Tuesday's AFCON 2027 qualifiers, Egypt put five goals past South Sudan, Guinea-Bissau shocked Nigeria 3-0, and Ivory Coast beat Somalia.
Ghana's goalkeeping coach Daniel Gaspar has expressed huge confidence in the Black Stars' options between the posts, claiming the national team has the best group of goalkeepers in Africa.
