diff --git a/ddtrace/_monkey.py b/ddtrace/_monkey.py
index 8dd83558c83..488211e46b1 100644
--- a/ddtrace/_monkey.py
+++ b/ddtrace/_monkey.py
@@ -173,17 +173,22 @@ def on_import(hook):
         path = "%s.%s" % (prefix, module)
         try:
             imported_module = importlib.import_module(path)
+            imported_module.patch()
+            if hasattr(imported_module, "patch_submodules"):
+                imported_module.patch_submodules(patch_indicator)
         except Exception as e:
             if raise_errors:
                 raise
-            error_msg = "failed to import ddtrace module %r when patching on import" % (path,)
-            log.error(error_msg, exc_info=True)
-            telemetry.telemetry_writer.add_integration(module, False, PATCH_MODULES.get(module) is True, error_msg)
+            log.error(
+                "failed to enable ddtrace support for %s: %s",
+                module,
+                str(e),
+            )
+            telemetry.telemetry_writer.add_integration(module, False, PATCH_MODULES.get(module) is True, str(e))
             telemetry.telemetry_writer.add_count_metric(
                 "tracers", "integration_errors", 1, (("integration_name", module), ("error_type", type(e).__name__))
             )
         else:
-            imported_module.patch()
             if hasattr(imported_module, "get_versions"):
                 versions = imported_module.get_versions()
                 for name, v in versions.items():
@@ -196,9 +201,6 @@ def on_import(hook):
                     module, True, PATCH_MODULES.get(module) is True, "", version=version
                 )
 
-            if hasattr(imported_module, "patch_submodules"):
-                imported_module.patch_submodules(patch_indicator)
-
     return on_import
 
 
diff --git a/releasenotes/notes/refactor-patch-error-ssi-1a2e9fe206d6d6df.yaml b/releasenotes/notes/refactor-patch-error-ssi-1a2e9fe206d6d6df.yaml
new file mode 100644
index 00000000000..8afc2e7595f
--- /dev/null
+++ b/releasenotes/notes/refactor-patch-error-ssi-1a2e9fe206d6d6df.yaml
@@ -0,0 +1,4 @@
+--- 
+fixes:
+  - |
+    Integrations: Improved error handling for exceptions raised during the startup of ddtrace integrations. This reduces the likelihood of the ddtrace library raising unhandled exceptions.
\ No newline at end of file
diff --git a/tests/telemetry/test_telemetry.py b/tests/telemetry/test_telemetry.py
index d767090f6d2..558e9961afc 100644
--- a/tests/telemetry/test_telemetry.py
+++ b/tests/telemetry/test_telemetry.py
@@ -243,14 +243,12 @@ def test_handled_integration_error(test_agent_session, run_python_code_in_subpro
     _, stderr, status, _ = run_python_code_in_subprocess(code, env=env)
 
     assert status == 0, stderr
-    expected_stderr = b"failed to import"
-    assert expected_stderr in stderr
+    assert b"failed to enable ddtrace support for sqlite3" in stderr
 
     integrations_events = test_agent_session.get_events("app-integrations-change", subprocess=True)
     assert len(integrations_events) == 1
     assert (
-        integrations_events[0]["payload"]["integrations"][0]["error"]
-        == "failed to import ddtrace module 'ddtrace.contrib.sqlite3' when patching on import"
+        integrations_events[0]["payload"]["integrations"][0]["error"] == "module 'sqlite3' has no attribute 'connect'"
     )
 
     # Get metric containing the integration error