At least one Iranian F-14 was shoot down by Iraqi MiG-23MLs, but I wouldn't consider that a fair combat. The Iranian F-14 was attempting to defect to Iraq and was mistakenly shot down by a pair of Iraqi MiG-23MLs. The Iraqi pilots were not aware the aircraft was defecting; they locked onto it and fired an R-24T missile, which destroyed the Tomcat.
The story of the Iraqi MiG-23 Flogger that mistakenly shot down an Iranian F-14 Tomcat that was defecting to Iraq
theaviationgeekclub.com
A few other Iranian F-14 loses have been
attributed to Iraqi MiG-23, but as far as I know not confirmed. Confirmed Iranian Tomcat losses in fair combat came from specialized tactical traps or encounters with French-built Iraqi Mirage F1s.