For both goals, Jenkinson could have done better, with former West Brom boss Steve Clarke and ex-Newcastle man Rob Lee criticising him for his positioning during the half-time analysis on Quest TV.
And it got worse for the 22-year-old, shown scratching his head, as he was nutmegged by Liverpool loanee Luis Alberto before conceding a penalty.
Thankfully for the Hammers, that spot-kick was missed, meaning they only trailed by two going into half-time.
Allardyce's men won their previous Schalke Cup clash (against hosts Schalke) on penalties, while Malaga beat Newcastle United 3-1.
All involved seemed fully aware, though, that this was Jenkinson's first game in West Ham colours - and only in a pre-season friendly.
The 22-year-old will likely improve with time - both physically and tactically - and could see plenty of first-team action at Upton Park this term.
Jenkinson was eventually replaced after an hour, when he hobbled off injured. The problem did not appear too serious, however, and is likely to be a pulled muscle of some kind.