Laudrup was dismissed on Tuesday amid concerns over the intensity of training and a lack of leadership from the Dane, with Garry Monk being appointed as head coach ahead of Saturday's south Wales derby against Cardiff.
The Swans have won just one of their last 10 Barclays Premier League fixtures and entered the weekend two points above the relegation zone.
And, in his programme notes for the game against Cardiff, Jenkins said: "Changing a manager mid-season is not always a wise choice unless, of course, there is good cause and solid reason.
"Collectively as a board we assessed every aspect surrounding the way our first-team staff and squad was working on a day-to-day basis.
"Without going into detail, it was clear to all of our directors that the strong principles we have had at Swansea City over the last 10 years were slowly being eroded.
"Only time will tell whether the timing was right, but in the end we had to get back to basics for the betterment of Swansea City.
"We need to work as one with a strong belief that we can compete with everyone in everything we do."
Laudrup has indicated he will take legal action against Swansea over his dismissal.