Yes. It seems lots of people have trouble understanding this, at least at first.
However, I think worries about this are overblown. Think this way. Suppose you use EUR to buy Apple shares at $310. Later you sell for $315, but EUR has appreciated against the USD, so although you gained $5 a share you actually get back less EUR than it cost to buy Apple shares - a loss. Is this totally a bad thing? Consider these things: (1) the exchange rate was equally likely to have gone the other way in which case you would have had a double gain - over the many transactions you will do as an investor, currency gains and losses will probably balance out, (2) your loss may be tax deductible against other gains, reducing the pain, (3) because the EUR is stronger you will now find that things you want to buy (say, New York hotel room, fuel for your car, shares in Amazon) may be cheaper in EUR terms.
Similar arguments can be made to demonstrate that a weakening of the EUR leading to a currency gain is not totally a good thing, eg (3) other things are now more expensive.