In order to understand what I listen, I'm trying to catch differences between "I walk to" and "I walked to" but I can't catch any difference. How can I distinguish that sounds?
It's almost impossible for native speakers to articulate the consonants /k/ /d/ /t in rapid succession with no intervening voiced vowel (even though some might think they do).
So in practice it's not worth trying to hear (or reproduce) a difference, because there usually isn't one. Just do the same as native speakers, and rely on context to tell you what was intended.
Arguably it's not fair to use an automated text-to-speech routine to illustrate this point, but it works for me. Try listening to this and this - if I don't look at the text, I've no idea which one is I walk to work and which is I walked to work.
Normally you wouldn't hear the difference, but a careful speaker might pronounce the 't' as a double consonant, i.e. hold the dental stop a trifle longer for 'walked to' than 'walk to'. Compare the double consonant sound 'n' in 'penknife', for example. If there had been a misunderstanding and the speaker was emphasising the past tense, they might make a double 't' sound, i.e. 't t', but this would not be the natural, unforced pronunciation.
As a native speaker I would say there's very little difference, but if there is any, it's in timing. Rather than there being an additional articulation of the "t" sound in "walked to", it's timed more closely to "walk" than to the vowel sound of "to". There may be differences in stress to depending on the context but I think these are hard to discuss in isolation.