SCT Controller providing OJT described a loss of separation event when traffic executing an approved missed approach procedure conflicted with other IFR traffic.

Narrative

I was conducting training on the Sector. We were slowly building in traffic and complexity but I felt that I was still in control and needed no assistance. We had approved an IFR Published Missed Approach procedure off of the ZZZ airport for the VOR-A Approach. The missed approach flies right through the south downwind of ZZZ1 Runway 24. We happened to have traffic on the south downwind for ZZZ1 and saw the conflict about 12 miles away. I told the trainee to climb the downwind traffic to 5;000 FT. The published missed approach also climbs to 5;000 FT; but I had planned to stop the missed approach aircraft at 4;000 FT which complies with MVA's and give vectors to the next airport. When the aircraft missed off of ZZZ our attention was somewhere else and the aircraft started his climb through 3;800 FT. By the time the aircraft checked in; the separation was lost. My trainee issued the traffic alert and started to reestablish applicable separation. I should have known better than to bet on the separation and getting communications in enough time. I will never again bet on anything and ensure separation at all times. Also; I should have called for a hand off long before the event happened. In the future I will ask for assistance as the traffic starts building and not wait until its too late.