I suggest to review the Tips and notes from the first lessons dealing with Czech pronunciation and orthography. D followed by I is actually a Ď and T followed by Ě is actually a Ť. There are several changes like that so I really recommend reviewing those Tips.
Ď is a voiced palatal stop /ɟ/, see https://en.wikipedia.org/wiki/Voiced_palatal_stop f
Ť is a voiceless palatal stop /c/, see https://en.wikipedia.org/wiki/Voiceless_palatal_stop for a thorough description including examples from other languages. It may sound to you like K if your language does not have this sound, but it is not the same at all. As an approximation, could try to produce a T followed by J (that means the English Y).
(sorry for the confusion of Ď and Ť in the first revision of this answer)