Stealing (and slightly modifying) @thei's example because it's so good:
"Israel should really change their policies to solve the Middle-East conflict."
"I resent the implication that the problems there are solely their fault."
I'm not aware of a good 1:1 translation for "resent the implication". The closest I can think of is
Die implizite Schlußfolgerung, Israel sei allein Schuld an dem Konflikt, ärgert mich.
depending on context, if in a heated discussion, one could also use "allegation" instead of "implication", and a stronger, more personal version of "resent":
Die Unterstellung, Israel sei allein Schuld an dem Konflikt, nehme ich Ihnen übel.
"In consequence, you are saying that the conflict is solely Israel's fault. I resent that."
To make it feel like natural German, one might change the sentence's structure a bit. This is what a strong supporter of Israel's policies might say in response in a discussion:
In der Konsequenz sagen Sie damit, Israel sei allein schuld an dem Konflikt. Das nehme ich Ihnen übel.
Other possible, not 100% literal translations for "resent" include
"Mag ich überhaupt nicht" (as shown by @deceze) - "I don't like it at all"
"ärgert mich" - "annoys me"
"Weise ich zurück", "Lehne ich ab" - "I reject the implication" - very un-personal, free from personal attack, might be the right thing to use in a formal setting