Playing a 6 strength card might be good in the first round if you can revive it with another card. Only play heroes to finish an enemy with a high number. If you play your 10 strength hero early and your enemy counters with 2 catapults and horn of command, you wasted it. You get more cards while your enemy loses some, making it easier to win the 2 other rounds. If you have multiple spys on your hand, spam them in the first round and let the enemy win.
Also, you might be able to purchase some cards from merchants. Mostly, these are innkeeper which give you powerful heroes (I highly recommend beating the innkeeper in oxenfurt, he gives you a yennefer card, 7 strenght, can revive someone from the graveyard) or good spell cards. After that, you start beating the guys which are your quest objectives. In the beginning, your goal should be to do a quest for zoltan where you receive 3 heroes which you can keep (you can also get a bit of money, but I highly recommend the cards!). You don't have a lot of powerful spells or heroes to really overpower an opponent. The starting deck is not really powerful without a lot of surprise cards. Basically, yes, you need a better deck to beat better opponents.
