You can do this with Leaflet. (I have done exactly this myself.)
You do have to convert your pixel sizes to latlong (latitude/longitude). Leaflet provides you an easy way to do that by using the Simple "Coordinate Reference System", map.project and map.unproject.
First, construct your map like this:
var map = L.map('map', {
maxZoom: 20,
minZoom: 20,
crs: L.CRS.Simple
}).setView([0, 0], 20);
…and then set the map bounds (for an image that is 1024x6145):
var southWest = map.unproject([0, 6145], map.getMaxZoom());
var northEast = map.unproject([1024, 0], map.getMaxZoom());
map.setMaxBounds(new L.LatLngBounds(southWest, northEast));
There's more details regarding splitting your images available here including a Ruby gem which might also be useful.