The Sea Robbers are flying the flag high on the continent as they are set to meet Etoile du Sahel in the CAF Confederation Cup Final next month.
Bucs also have a Telkom Knockout quarter-final date with Maritzburg United on Saturday.
However, Tinkler's men are 11th on the Absa Premiership table with five points from six games - 11 points adrift of leaders Bidvest Wits, and a point above the drop zone.
"The chairman [Irvin Khoza] has reiterated to the players the importance of replicating our CAF form domestically. It has been addressed," Tinkler said.
"As a coach of Orlando Pirates you are always going to be under pressure and it's something I've understood from the beginning.
"Your job is never secure. It's part and parcel of being a coach."
He added: "We are concerned with the form we are showing in the League but it's something that can be rectified by us as a group."