Though even saying that occasionally depending on the stature of a series even titles from the 90's downwards don't feel that old since they have continued to prosper. For example the Ghibli films, Cowboy Bebop, Evangelion, Trigun etc. As a 80s/90s kid I grew up on Cel animation so the look doesn't inherently feel old.
So perhaps it's more the style of storytelling, the music and the character designs. With all those combined I can definitely get the feeling I'm watching something old. The decade be it 90's, 80's or 70's doesn't really matter I think it's more those 3 factors that make something old fashioned. For example Future Boy Conan doesn't feel old, it's basically a 10 hour Ghibli film so I like to think of it as retro rather than old. Speed Racer and Astroboy now those feel old haha.
I guess after trying to put down my thoughts I don't really have a clear opinion, I have enjoyed Anime from many decades and many shows have captivated me just as much as any modern show has done. So I suppose it's on a show by show basis, some things stand the test of time and still feel fresh and new and others haven't and instead feel old and outdated. It's the same as movies or music that way.