It does require a bit of luck.  I'm always kicking myself when I lose a cool wild because I chose the wrong option.  Take a look at the wiki page https://horsefable.wiki/explore/wild-horses/ on wilds for some info, but I'll tell you what I've learned from experience.

• Watch your energy.  Each pet attempt costs energy so if a wild pops up while you have little or no energy it might be best to page away for a little bit and come back with more
• I've had pretty bad luck with lassos. Sometimes they lower the wild essence(bar on the side) but mostly they just drop the bond(bar on the top with percentage) you've built up with the horse or even make them run away instantly.  Use them as a last resort or if you can sacrifice a little bit of bond.
• Whistles are valuable but I wouldn't try them right off the bat unless you have no other options.  Build a bit of a bond first then whistle, usually if there's a negative reaction to it it only drops the bond.  Sometimes they bolt though, it's chancy.
• Treats are INVALUABLE, they are simply the best way to catch wilds but you have to be using the right kind!  You can look at this helpful thread here to see which horses like which treat if you don't want to experiment on your ow   https://horsefable.com/topic/6870/ Also try not to use the raw materials on wilds, it's way more worth it to save them to craft your own treats & sweet treats, though if you have a surplus of say apples it couldn't hurt to chuck a few at the wild.  Keep in mind though treats are not a guarantee capture.  I have had wilds bolt on me when I'm feeding them their favorites.
• I alternate between treats and petting.  Seems to work okay, if the horse doesn't like the pet the treat recovers the bond.  Stop petting if the horse repeatedly dislikes it.
• Be choosy about the wilds you catch if you are low on treats, energy or whistles.  It can be disappointing to catch a regular plain Jane bay 3 star horse of a breed you don't much care about with your last treats only to encounter a skewed horse of a breed you love minutes later.  Unless you're trying to speedrun the wild horse catching achievement there's no reason to attempt every horse.  Sometimes I see the horse is lower stars or I'm otherwise not interested and I just shoo immediately so all I've spent is energy to glance at it.
• If a horse is being stubborn and isn't a 5 star breed you want desperately to catch or color you deeply love, shoo it after a few failed attempts. Again, don't waste resources on horses you don't actually want.

As far as I know there's no item or method that will 100% catch a horse so best you can do is keep trying different things until something works for you based on your resources and luck.  I wish you good luck on your next attempt!

Tacking onto the above; whilst lassos are supposed to have a purpose, plenty of older players will say that there isn't any purpose.

Whistles? Can SOMETIMES instant catch a horse, but in my experience? That never happens, so I always sell mine. Others have has better experience.

Using the provided link above, is usually a better guarantee. Since it was a pony build, they prefer Alfalfa based treats. Never flat out just give them Alfalfa, craft it into say Apple Alfalfa treats or Sweet Apple Alfalfa treats, using Molasses there. Crafting does cost bits, so be mindful of this too.

As well, I prefer not to use petting, as at my stage, I have plenty of treats, picked up and enough crafted treats, that I reserve my energy for continuing on exploring.

Maybe for the time being, IGNORE any wild horse you find. Save up on seasonal dyes, like Sunburn, Bubblegum, Teal, etc to sell to other players for bits, which you could possibly turn around and buy treat items from other players via the Marketplace.

Once you have enough crafted treats saved up? I'd least say 10 of each NOT sweet, you may be able to try catching wilds. Molasses can be trickier to come by, but having a base and knowing what body type, each wild prefers, can usually yield better results, but even for me? I've still had them run from me, unfortunately.

No, I use my dyes on my horses. I don't want to sell my dyes. They are hard to come by.