Ferguson, who won the Champions League twice, the league 13 times and five FA Cups with United, was among those who backed Parker to succeed in his new role.
"I don't have many friends but yesterday my phone was pinging all the time," Parker, a coach at Fulham since July last year, told a news conference.
"Sir Alex (Ferguson) texted me which was incredible. To think he spent the time to write a long detailed message giving me advice on how he sees things was truly inspirational.
"We all understand the football world, there's times when things are going well and you see the love."
Parker said he had mixed emotions following the sacking of Ranieri who arrived in November to replace Slavisa Jokanovic but lasted 16 league games.
"He came in and had open arms with me in the sense of helping and I'd like to think I helped him at times. On the flip side of that, (feelings) of excitement," the 38-year-old added.
"I appreciate the opportunity which the owners have given me here. It's a big job but I'm really looking forward to it."
Following the Chelsea game, promoted Fulham face potentially difficult tests against Ranieri's former side Leicester City, leaders Liverpool and champions Manchester City this month.
"The situation doesn't lie, it's a tough one. Regarding those games, this is a bunch of players that last year were one of the best teams in the Championship," Parker said.
"I think my main focus is to get a balance back. When you lose a lot, things can go off on different tangents and I feel that's where we are... we need to regroup and I know if we do that, results will be a byproduct.
"At times this year we've been easy to play against and that's why fans have pulled away a bit... we need to change... and address that in the coming weeks."
Fulham are 19th in the league with 17 points from 28 games.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
