Is there a counterpart of "sufficient"/"enough" meaning "not more than the needed maximum"?

Quite simply "not in excess".

Since excess means:

An amount of something that is more than necessary, permitted, or desirable:

and in excess means:

Exceeding the proper amount or degree

(from ODO)

So if something is in excess then it is more than sufficient.

By the same definition you have given:

sufficient = enough to meet the needs of a situation or a proposed end

But in my opinion that does not translate to:

not less than the needed minimum

But rather to:

not less than the needed minimum AND no more than the allowed maximum

As in your case, exceeding such limit doesn't allow you to meet the needs or requirements of your situation. So I would still say that 94% concentration is sufficient. However, if you prefer, you could say that the concentration is within parameters o within limits. Also, perhaps you can say that it is an acceptable, tolerable or adequate concentration, to imply that it is within limits.

You could say the 94% concentration is effective. However, this doesn't really address whether it's possible to have too much, or too little, or both. It won't lead to any incorrect interpretations, though.

I think “sufficient” covers the whole range between insufficiently low (too low) and insufficiently high (too high), but I do agree that “sufficient” (and especially “enough”) can imply that the lower end of that range has been (just barely?) reached.

Just as, imo, “sufficient” covers the whole acceptable/sufficient range (with a bias towards the low end), so does “tolerable” cover the whole acceptable/tolerable range, but perhaps with the bias towards the high end that you are seeking.

“Tolerable”: adjective/ bearable, endurable, supportable, acceptable. (Oxford Dictionnaires)

Step 1: Insufficiently low/intolerably low (too low) = insufficient/intolerable/unacceptable);

Step 2: Sufficiently high/tolerably low (high enough/not too low) = sufficient/tolerable/acceptable;

Step 3: Tolerably high/sufficiently low (not too high/low enough) = tolerable/sufficient/acceptable;

Step 4: Intolerably high/insufficiently high (too high) = intolerable/insufficient/unacceptable.

The above steps are trying to show that “insufficient, sufficient, tolerable, and intolerable” can be used at both ends of the range of acceptability, but please note that the bolded words in each step are, in my opinion, ‘best suited for’/most often associated with that step.

Both “insufficiently” and “intolerably” use “low” in Step 1 and “high” in Step 4 to convey the meaning of those two Steps, which could mean that the bias towards either the low end (sufficient) or the high end (tolerable) that I perceive in these two words disappears when discussing unacceptable levels below and above the acceptable range.

Within the range of acceptability, however, “high” and “low” must be flipped to make sense of “tolerable” and “sufficient” as they are used in Steps 2 and 3, which, imo, supports the bias that I perceive and perhaps supports “tolerable” as the best one-word answer to your question.