The proscription against using too many adverbs is greatly misunderstood. It's not using too many that's a problem - it's how you use them.
Adverbs become irritating when they add nothing to the verb, and by extension to the sentence, when they reinforce something which is already clear from the action or dialogue, and merely intensify the verb rather than change it. Adverbs are fine when they modify the verb so much that the sentence would have a different meaning without the adverb.
I once read a book in which two characters were having an argument, and a line of dialogue attribution read "she said snippily." This was just bad writing, because her tone of voice and intention were already clear from the line of dialogue and the context. Bad adverb.
A good adverb adds something to the verb or sentence which is otherwise absent. For example: "smiled sadly" - sadly completely changes the meaning of smiled. I can't think of any more complex examples of this right now because it's very dependent on context, but hopefully you get the idea.
The other pitfall with adverbs is making them up. If you use adverbs then make sure they're words you (or the POV character) might actually use to describe concrete things - slowly, carefully, grudgingly, widely - not made up adverbs to reinforce how a particular action is done.
Another example. Say you want to write that a character "walked slowly and carefully". In this case I'd strip the adverbs and replace it with "inched" or "edged" or "crept" depending on the situation, because we know what those things are. Now imagine you want to write the same character slowly and carefully opening a box. There's no specific verb I can think of for slowly and carefully opening a box, it's too specific, so use the adverbs because they add something which would otherwise be absent.
Context is key.