An antivirus detects only so and so much ("During 4Q11, 33 percent of Web malware encountered was zero-day malware not detectable by traditional signature-based methodologies at the time of encounter", source: http://blogs.cisco.com/security/cisco-4q11-global-threat-report/ ).
With a bit of training you can detect some malware because they behave in a certain way that is a bit off to whats usual on the OS. It might be more network traffic, more cpu usage, strange disk accesses or something else. Malware are not only available as single binaries which are detectable via a taskmanager but also as dynamic libraries (dll) attached to other processes.
You can get clues about what is running on your system with a taskmanager like Process Explorer from the Sysinternal Suite, and you can watch things happen on your system with something like Process Monitor of the same suite. Get used to the tools and watch for signs of "strangeness":
- Unsigned binaries (executables or dlls)
- Strange writes to strange files
- Strange network activity
(The "strange" part is the training you need in order to distinguish between "that's normal" and "that is strange")
The author of the Sysinternal Suite shows some clever ways to use the above mentioned tools:
So, yes, you can detect some of the malware with a decent task manager. The less sophisticated the malware is, the easier it will be to detect. If the malware tries to detect the use of task managers like Process Explorer you might need to even take advanced steps such as using a different "Session" to detect strange behavior but it is still possible.