Vuejs Search filter

You could use computed property for this case, so, i created one called filteredResources which will be used in v-for loop, i had used dummy data, but you could keep your resources declared empty and call a promise function to fill it in created hook, check this code if your are preferring single file component or the following code of you're using Vue via CDN

new Vue({
  el: '#app',
  data() {
    return {
      searchQuery:'',
    resources:[
    {title:"aaa",uri:"aaaa.com",category:"a",icon:null},
     {title:"add",uri:"aaaa.com",category:"a",icon:null},
      {title:"aff",uri:"aaaa.com",category:"a",icon:null},
    {title:"bbb",uri:"bbbb.com",category:"b",icon:null},
    {title:"bdd",uri:"bbbb.com",category:"b",icon:null},
    {title:"bsb",uri:"bbbb.com",category:"b",icon:null},
    {title:"ccc",uri:"cccc.com",category:"c",icon:null},
    {title:"ddd",uri:"dddd.com",category:"d",icon:null}
    ]
    };
  },
  computed: {
    filteredResources (){
      if(this.searchQuery){
      return this.resources.filter((item)=>{
        return item.title.startsWith(this.searchQuery);
      })
      }else{
        return this.resources;
      }
    }
  }
 

})
<!DOCTYPE html>
<html>
<head>
<meta name="viewport" content="width=device-width, initial-scale=1">
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.16/vue.js"></script>
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.1.3/css/bootstrap.min.css" >

</head>
<body>
<div id="app">

   <div class="panel panel-default">
                <div class="panel-heading" style="font-weight:bold"><span class="glyphicon glyphicon-align-justify"></span> All Resources</div>
                <div class="row">
                    <div class="search-wrapper panel-heading col-sm-12">
                        <input class="form-control" type="text" v-model="searchQuery" placeholder="Search" />
                    </div>                        
                </div>
                <div class="panel-body" style="max-height: 400px;overflow-y: scroll;">
                    <table v-if="resources.length" class="table">
                        <thead>
                            <tr>
                                <th>Resource</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr v-for="item in filteredResources">
                                <td><a v-bind:href="item.uri" target="_blank">{{item.title}}</a></td>
                            </tr>
                        </tbody>
                    </table>
                </div>
            </div>
</div>

</body>
</html>

You can use the includes() function of the array to search any position in a sentence or phrase.

new Vue({
  el: '#app',
  data() {
    return {
        searchQuery: null,
        resources:[
            {title:"ABE Attendance",uri:"aaaa.com",category:"a",icon:null},
            {title:"Accounting Services",uri:"aaaa.com",category:"a",icon:null},
            {title:"Administration",uri:"aaaa.com",category:"a",icon:null},
            {title:"Advanced Student Lookup",uri:"bbbb.com",category:"b",icon:null},
            {title:"Art & Sciences",uri:"bbbb.com",category:"b",icon:null},
            {title:"Auxiliares Services",uri:"bbbb.com",category:"b",icon:null},
            {title:"Basic Skills",uri:"cccc.com",category:"c",icon:null},
            {title:"Board of Trustees",uri:"dddd.com",category:"d",icon:null}
        ]
    };
  },
  computed: {
    resultQuery(){
      if(this.searchQuery){
      return this.resources.filter((item)=>{
        return this.searchQuery.toLowerCase().split(' ').every(v => item.title.toLowerCase().includes(v))
      })
      }else{
        return this.resources;
      }
    }
  }
 

})
<!DOCTYPE html>
<html>
<head>
<meta name="viewport" content="width=device-width, initial-scale=1">
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.16/vue.js"></script>
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.1.3/css/bootstrap.min.css" >

</head>
<body>
<div id="app">
   <div class="panel panel-default">
   <div class="panel-heading">
         <strong> All Resources</strong></div>
            <div class="row">
                 <div class="search-wrapper panel-heading col-sm-12">
                     <input class="form-control" type="text" v-model="searchQuery" placeholder="Search" />
                </div>                        
            </div>
        <div class="table-responsive">
            <table v-if="resources.length" class="table">
                <thead>
                    <tr>
                         <th>Resource</th>
                    </tr>
                </thead>
                <tbody>
                    <tr v-for="item in resultQuery">
                        <td><a v-bind:href="item.uri" target="_blank">{{item.title}}</a></td>
                    </tr>
                </tbody>
            </table>
        </div>
   </div>
   </div>

</body>
</html>

Based on this answer → Vue.js search keyword in array