The 33-year-old has left Oxford City to replace former Wood boss Luke Garrard, who stepped away after nearly nine years at the helm.
Wood enjoyed historic success under Garrard, reaching the play-offs three times including the promotion final in 2018.
But last year's struggle - that resulted in relegation to Step 2 has triggered a changing of the guard and Jenkins, who won promotion with City through the play-offs in 2022-23, is embracing the expectation.
"The target is on every club's back really," Jenkins told The NLP. "You look at the clubs in the league. There's ourselves, Dorking, Maidstone, Torquay, Worthing got into the final, the Baths of this world - there's targets on everyone's back because every club wants to progress and do well.
"It's important we focus on ourselves and really fine-tune things this season and use that in a positive manner - we need to go out and show teams and other players we mean business. We want to play attractive football but we also want to win games of football.
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