这个问题可能是由于您的API网关集成配置中存在错误引起的。在API集成的设置中，您需要将集成类型设置为AWS服务，并选择目标为EventBridge。下面是一个示例集成配置：

"resources": [
{
    "path": "/myApi",
    "httpMethod": "POST",
    "integration": {
        "type": "AWS",
        "uri": "arn:aws:apigateway:us-east-1:events:action/PutEvents",
        "passthroughBehavior": "when_no_templates",
        "httpMethod": "POST",
        "requestTemplates": {
            "application/json": "{\n  \"detail\": $input.json('$'),\n  \"detail-type\": \"My Detail Type\",\n  \"source\": \"com.mycompany.myapp\"\n}"
        },
        "credentials": "arn:aws:iam::1234567890:role/MyRole",
        "integrationResponses": [
            {
                "statusCode": "200"
            }
        ]
    }
}

请确保uri正确设置为arn:aws:apigateway:{Region}:events:action/PutEvents并且credentials正确指向一个允许PutEvents操作的角色。如果您已经使用了正确的集成配置，但仍然遇到此错误，请确保您的IAM用户或角色具有PutEvents操作的权限。