The Swans continue their Europa League campaign on Thursday when they tackle Russian side Kuban Krasnodar, having made a flying start with victories over Valencia and St Gallen.
Those results have proved an extension of the outstanding work Laudrup has done on a domestic stage, highlighted by winning the League Cup last term.
"In the time he has been here, Michael has proved how important he is," Jenkins told the club's official website.
"I think he has brought different qualities and we've adapted as a team and as players.
"I think they've all grown and developed a little bit more responsibility in what they do, which Michael encourages.
"I think he has brought a winning mentality - he showed that last year when we won the League Cup - and I've no doubt he is going to try to push and get us as far as we can this year in the Europa League.
"He's been a key ingredient and he's a good man to work with - honest and trustworthy - and he's got the same beliefs as us, so the relationship is a good one."