I would argue otherwise. A Link to the Past is basically a really glamorous Zelda 1, with a highly advanced engine and better graphics and improved gameplay methods, all that. Link's Awakening added another dimension with the numerous side quests, trade exchanges, secret locations, side plots, and the depth of story.
A Link to the Past was basically all fighting and puzzle solving, with few things to do outside of it (almost everything you did outside of the dungeon led you right to the next dungeon). I think Ocarina took a lot of influence from Link's Awakening, in that sense.
Not to say they're not influenced by A Link to the Past. Of course they are, and heavily at that. But I think that influence is mostly carry-over from the first game, which established that method of gameplay. A Link to the Past heavily improved upon it, but Link's Awakening and Ocarina of Time were the games that really changed it into what it is today, by adding the things that they did.