The Hammers lost 4-3 against Bournemouth at Upton Park, with Jenkinson at least partly at fault for two of the goals that they conceded in the contest.
It was a display which was well below standard for the Arsenal loanee, but he says that Bilic knew that he did not need to read the riot act to him after it happened.
“Everyone has a bad day at the office, you just get on with it," he said. "That’s life and it is about how you respond. The boss didn’t say a lot, he knows what sort of person I am and that I am not going to dwell on it and that is what I have done.”
Since that match, Jenkinson has lost his place in the team - and he was left on the substitutes' bench in the Hammers most recent fixture against Newcastle United.
However, there is still hope for the rapid right-back, as he was called to come on to replace Angelo Ogbonna during the match against the Magpies, and put in a solid performance, helping his side claim the three points in a 2-0 success.
It was a display more in line with the quality of those that he was putting in last season, and a reminder of the skill that he does have.
Jenkinson will now be aiming to stay in the starting line-up, with the Hammers in good form over the early part of the new campaign.