diff --git a/changelogs/fragments/78781-fix-apt-only_upgrade-behavior.yml b/changelogs/fragments/78781-fix-apt-only_upgrade-behavior.yml
new file mode 100644
index 00000000000..5b54bf89056
--- /dev/null
+++ b/changelogs/fragments/78781-fix-apt-only_upgrade-behavior.yml
@@ -0,0 +1,4 @@
+bugfixes:
+- >-
+  apt - Fix module failure when a package is not installed and only_upgrade=True.
+  Skip that package and check the remaining requested packages for upgrades. (https://github.com/ansible/ansible/issues/78762)
diff --git a/lib/ansible/modules/apt.py b/lib/ansible/modules/apt.py
index b254fb031e1..08b3e147296 100644
--- a/lib/ansible/modules/apt.py
+++ b/lib/ansible/modules/apt.py
@@ -711,7 +711,12 @@ def install(m, pkgspec, cache, upgrade=False, default_release=None,
         package_names.append(name)
         installed, installed_version, version_installable, has_files = package_status(m, name, version_cmp, version, default_release, cache, state='install')
 
-        if (not installed_version and not version_installable) or (not installed and only_upgrade):
+        if not installed and only_upgrade:
+            # only_upgrade upgrades packages that are already installed
+            # since this package is not installed, skip it
+            continue
+
+        if not installed_version and not version_installable:
             status = False
             data = dict(msg="no available installation candidate for %s" % package)
             return (status, data)
diff --git a/test/integration/targets/apt/tasks/repo.yml b/test/integration/targets/apt/tasks/repo.yml
index e4e39aa3570..d4cce78a1b0 100644
--- a/test/integration/targets/apt/tasks/repo.yml
+++ b/test/integration/targets/apt/tasks/repo.yml
@@ -54,7 +54,7 @@
 
 # https://github.com/ansible/ansible/issues/30638
 - block:
-  - name: Fail to install foo=1.0.1 since foo is not installed and only_upgrade is set
+  - name: Don't install foo=1.0.1 since foo is not installed and only_upgrade is set
     apt:
       name: foo=1.0.1
       state: present
@@ -67,30 +67,36 @@
     assert:
       that:
         - "apt_result is not changed"
-        - "apt_result is failed"
+        - "apt_result is success"
 
   - apt:
       name: foo=1.0.0
       allow_unauthenticated: yes
 
-  - name: Upgrade foo to 1.0.1
+  - name: Upgrade foo to 1.0.1 but don't upgrade foobar since it is not installed
     apt:
-      name: foo=1.0.1
+      name: foobar=1.0.1,foo=1.0.1
       state: present
       only_upgrade: yes
       allow_unauthenticated: yes
     register: apt_result
 
   - name: Check install with dpkg
-    shell: dpkg-query -l foo
+    shell: "dpkg-query -l {{ item }}"
     register: dpkg_result
+    ignore_errors: yes
+    loop:
+      - foobar
+      - foo
 
   - name: Check if install was successful
     assert:
       that:
         - "apt_result is success"
-        - "dpkg_result is success"
-        - "'1.0.1' in dpkg_result.stdout"
+        - "dpkg_result.results[0] is failure"
+        - "'1.0.1' not in dpkg_result.results[0].stdout"
+        - "dpkg_result.results[1] is success"
+        - "'1.0.1' in dpkg_result.results[1].stdout"
   always:
     - name: Clean up
       apt: