Simpson has spoken out to defend his decision to hand the post to the 35-year-old former Chelsea reserve-team coach, claiming he was the Hornets' first-choice to succeed Adrian Boothroyd, whom he sees several similarities with.
He told BBC Three Counties Radio: "We haven't brought him in for the next six games or the next three months.
"We have brought him in because we believe he is the right person to take us forward over a number of years.
"I would ask supporters to give him a chance.
"He won't turns things around overnight. It's about putting down strong foundations, building on the work that has been done, and it will take time."
He added: "It's fair to say he was on our radar from day one.
"We had done our homework on him, but we had 50 applications and we interviewed eight people."
Simpson also confirmed Rodgers is fully aware that the Hornets are not in a fantastic financial situation so funds for new faces will be very limited.
He said: "You don't bring any manager on board and tell lies. You tell him how it is, and although we are not in a wonderful position we are not in a bad position compared with many other Championship clubs.
"We are making sure we are sensible going forward as we come out of parachute payments at the end of this season. I have explained that to Brendan, he's taken that on board completely, and he knows what he's coming into."
On the similarities between Rodgers and former boss Boothroyd, he concluded: "They both have ambition and focus, but Brendan has been working for 15 years to achieve this having been forced to retire from playing at the age of 20.
"Of course his experience at Chelsea has made the headlines, but his time at a community club like Reading is also a key factor for us."
Malky Mackay will remain in charge for the game at Bristol City on Tuesday night before making way for the new man for Saturday's clash with Doncaster.