Warnock's team beat Kilmarnock 3-1 at Pittodrie, but the club announced the 75-year-old had "stepped aside" soon after the final whistle in the quarter-final clash.
Warnock was hired by Aberdeen on February 5th with the former Sheffield United boss accepting the job until the end of the season.
He had replaced the sacked Barry Robson in the hope of lifting struggling Aberdeen away from the relegation zone but did not earn a single win in his six Scottish Premiership matches.
Aberdeen chairman Dave Cormack said: "The club would like to thank both Neil and Ronnie Jepson for their efforts.
"With the search for a new manager at an advanced stage, Peter Leven will assume control of all first-team matters until the process is concluded."
Warnock came out of retirement last year and kept relegation-threatened Huddersfield in the English Championship but left the job in September.
The former Crystal Palace and QPR boss has won eight promotions and holds the record for the most league games managed in England, with 1,626 matches during his time at 15 clubs.
