diff --git a/CHANGELOG.md b/CHANGELOG.md
index 13fac64..f999f0f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,12 @@
 # Changelog
 
+## [1.4.1](https://github.com/googleapis/python-network-connectivity/compare/v1.4.0...v1.4.1) (2022-07-13)
+
+
+### Bug Fixes
+
+* **deps:** require google-api-core>=1.32.0,>=2.8.0 ([#190](https://github.com/googleapis/python-network-connectivity/issues/190)) ([7b0e8a6](https://github.com/googleapis/python-network-connectivity/commit/7b0e8a6e3283a7cda78e6a75ce898e8f096ce1ce))
+
 ## [1.4.0](https://github.com/googleapis/python-network-connectivity/compare/v1.3.2...v1.4.0) (2022-07-06)
 
 
diff --git a/setup.py b/setup.py
index 868593c..13129cf 100644
--- a/setup.py
+++ b/setup.py
@@ -20,7 +20,7 @@
 
 import setuptools  # type: ignore
 
-version = "1.4.0"
+version = "1.4.1"
 
 package_root = os.path.abspath(os.path.dirname(__file__))
 
@@ -45,7 +45,7 @@
     platforms="Posix; MacOS X; Windows",
     include_package_data=True,
     install_requires=(
-        "google-api-core[grpc] >= 2.8.0, <3.0.0dev",
+        "google-api-core[grpc] >= 1.32.0, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*",
         "proto-plus >= 1.15.0, <2.0.0dev",
         "protobuf >= 3.19.0, <4.0.0dev",
     ),
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index f74740e..b450739 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -19,6 +19,6 @@
 #
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
-google-api-core==2.8.0
+google-api-core==1.32.0
 proto-plus==1.15.0
 protobuf==3.19.0