Use Response parameters.

aiogram/exceptions.py

@@ -1,3 +1,7 @@
+from aiogram import types
+from .utils import json
+
+
 class ValidationError(Exception):
     pass
 
@@ -9,3 +13,18 @@ class TelegramAPIError(Exception):
         self.method = method
         self.status = status
         self.body = body
+
+    def json(self):
+        if not self.body:
+            return None
+        try:
+            data = json.dumps(self.body)
+        except Exception:
+            data = None
+        return data
+
+    @property
+    def parameters(self):
+        data = self.json()
+        if data and 'parameters' in data:
+            return types.ResponseParameters.deserialize(data['parameters'])