With a sharp knife diagonally cut carrots into scant 1/8-inch-thick slices and cut slices lengthwise into julienne strips. In a bowl stir together water, vinegar, sugar and salt until sugar is dissolved. Add carrot and marinate 5 minutes.
Drain carrot in a sieve, discarding marinade. Cut romaine crosswise into 1/4-inch-wide strips and in a bowl toss with carrot, oil, celery seeds, and salt and pepper to taste.