Francesca, let me try to explain this by making a comparison with your native Italian. Present Perfect in English is very different from Italian. The Italian version truly is a tense (dealing with timeframe), but the English version is not. The Italian version, unlike the English, can place an action in the past. The English version lacks this capacity. The only time information it provides is that which is given by the present tense of the verb "to have".
It makes sense in Italian to say "Ieri sono andato al parco e lì ho mangiato del cioccolato". In English, this would be nonsense: "Yesterday I have gone to the park and there I have eaten some chocolate". The reason it is nonsense is that "I have gone" means "I now have experience of going", and "I have eaten" means "I now have experience of eating". Therefore, in English this would say
"Yesterday, I now have the experience of going to the park and there I now have the experience of eating some chocolate."
Do you see how strange that might sound to us? The sentence starts in the past with "yesterday", but jumps to the present "I now have". It would be just as strange as saying "Yesterday I am happy right now".
Your original sentence means
"I now have the experience of trying to change his mind, but I did not succeed."
This sentence has no timeline problem. The sentence starts by telling an experience that you now have, and finishes by telling what happened in the past. A simpler example would be "I have eaten chocolate, but I did not like it". It is crystal clear.