Our first couple games went very similar to that. Virtually every time we play now though, the humans have dominated. Which is the opposite problem I guess.
A large mistake we made in our first game was that we had zombies moving double speed. Don't know how we looked over that in the rules, but make sure you only have zombies moving one space. Ignoring the use of special cards of course. Note that the human players ran roll a die to see how far they would be able to move before choosing to search or run. There's been many a time a player has chosen to stay and search rather than run a futile single space. Make sure that the Zombie Player is evenly distributing zombies within a single spawn among their spawning pits. Don't forget that the Manor House is only in play during the 'Protect the Manor' Scenario. Otherwise it's the big open field. I've found the Manor scenario to a harder, if not the hardest, scenario to win as the Humans by the way. The Zombie player is limited to a hand of four cards, a good number of which involve combat. The less you are in combat, the fewer chances the Zombie player has to use the cards. So if they want new cards, they'll have to discard those combat events (good for the humans) or hold onto the cards and not draw new ones (also good for you, reduces the changes of getting a 'Play Immediately' event)
An important thing to consider is that if the scenario you're playing doesn't directly involve killing zombies, it may be better to leave zombies alone if you have the option. Especially since actually killing zombies with a melee weapon doesn't have very good odds. Left to their own devices, the humans will find what they need to get out easily, so the Zombie Player isn't going to be holing up somewhere protecting an area; he just doesn't have the resources to both guard an important area while also putting pressure on the humans. So you're going to be pursued most of the time already, why make it easier to be caught? If you're running from one side of the map to the other and pick off a zombie with a ranged weapon just because you can, this gives the Zombie Player a new figure to work with and they can just spawn them closer to where you were going anyway. Unnecessarily fighting/shooting zombies also gives you a chance to get hurt through combat or lose your weapon (either by running out of bullets or through a Zombie Player card). A human would need four dice to a Zombie's one to have better odds of killing it then getting hurt from the attempt. Plus the zombie player has cards to force rerolls and add additional dice to the zombies. Unless you have found an Instant Kill weapon like the butcher knife (which auto-kills if any of your dice show a 6, regardless of what the Zombie player rolls), survivability-wise, it's always better to run.
If the scenario you're playing involves finding specific items, searching buildings is the top priority. You can spend all day killing Zombies, but unless you find the keys and gas, you can't escape in the car, so get to searching! Having the Survivors stick in pairs (while this does make them potential targets for cards like 'This Could Be Our Last Night on Earth') allows you to split up groups of attacking zombies and allows for other strategies, like healing each other, trying to lure zombies away, etc. Make sure you remember though that each Survivor has to fight all the Zombies in their space when they end their turn, even if they're in the same space as someone else. You can only divide the Zombies between Survivors during the Zombie Player turn. Zombie Hunger can be a useful trait to use against to Zombie Player. If a human is within one space of a zombie, the zombie has to move to a human (Zombie Player choice if there are multiple spaces). If a zombie shares a space with a human, it cannot leave. There has also been many human sacrifices to allow another player with a scenario item to escape a building. Remember though, even superior strategy is subject to the whims of the dice gods. Zombies winning ties