diff --git a/moto/secretsmanager/exceptions.py b/moto/secretsmanager/exceptions.py
index 746368a6b..d4563dc42 100644
--- a/moto/secretsmanager/exceptions.py
+++ b/moto/secretsmanager/exceptions.py
@@ -15,6 +15,15 @@ class ResourceNotFoundException(SecretsManagerClientError):
         )
 
 
+class SecretNotFoundException(SecretsManagerClientError):
+    def __init__(self):
+        self.code = 404
+        super(SecretNotFoundException, self).__init__(
+            "ResourceNotFoundException",
+            message=u"Secrets Manager can\u2019t find the specified secret."
+        )
+
+
 class ClientError(SecretsManagerClientError):
     def __init__(self, message):
         super(ClientError, self).__init__(
diff --git a/moto/secretsmanager/models.py b/moto/secretsmanager/models.py
index 6ecc32935..2a3e7ede4 100644
--- a/moto/secretsmanager/models.py
+++ b/moto/secretsmanager/models.py
@@ -11,6 +11,7 @@ import boto3
 from moto.core import BaseBackend, BaseModel
 from .exceptions import (
     ResourceNotFoundException,
+    SecretNotFoundException,
     InvalidParameterException,
     ResourceExistsException,
     InvalidRequestException,
@@ -47,7 +48,7 @@ class SecretsManagerBackend(BaseBackend):
     def get_secret_value(self, secret_id, version_id, version_stage):
 
         if not self._is_valid_identifier(secret_id):
-            raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+            raise SecretNotFoundException()
 
         if not version_id and version_stage:
             # set version_id to match version_stage
@@ -57,7 +58,7 @@ class SecretsManagerBackend(BaseBackend):
                     version_id = ver_id
                     break
             if not version_id:
-                raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+                raise SecretNotFoundException()
 
         # TODO check this part
         if 'deleted_date' in self.secrets[secret_id]:
@@ -176,7 +177,7 @@ class SecretsManagerBackend(BaseBackend):
 
     def describe_secret(self, secret_id):
         if not self._is_valid_identifier(secret_id):
-            raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+            raise SecretNotFoundException()
 
         secret = self.secrets[secret_id]
 
@@ -205,7 +206,7 @@ class SecretsManagerBackend(BaseBackend):
         rotation_days = 'AutomaticallyAfterDays'
 
         if not self._is_valid_identifier(secret_id):
-            raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+            raise SecretNotFoundException()
 
         if 'deleted_date' in self.secrets[secret_id]:
             raise InvalidRequestException(
@@ -347,7 +348,7 @@ class SecretsManagerBackend(BaseBackend):
     def delete_secret(self, secret_id, recovery_window_in_days, force_delete_without_recovery):
 
         if not self._is_valid_identifier(secret_id):
-            raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+            raise SecretNotFoundException()
 
         if 'deleted_date' in self.secrets[secret_id]:
             raise InvalidRequestException(
@@ -377,7 +378,7 @@ class SecretsManagerBackend(BaseBackend):
             secret = self.secrets.get(secret_id, None)
 
         if not secret:
-            raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+            raise SecretNotFoundException()
 
         arn = secret_arn(self.region, secret['secret_id'])
         name = secret['name']
@@ -387,7 +388,7 @@ class SecretsManagerBackend(BaseBackend):
     def restore_secret(self, secret_id):
 
         if not self._is_valid_identifier(secret_id):
-            raise ResourceNotFoundException(u"Secrets Manager can’t find the specified secret.")
+            raise SecretNotFoundException()
 
         self.secrets[secret_id].pop('deleted_date', None)