The Whites went into the game at Craven Cottage as underdogs but were clearly buoyed by their 2-2 draw against Manchester United on Sunday.
A Kolo Toure own goal and a close-range Kieran Richardson finish had put Meulensteen's side ahead twice, only for Liverpool to secure a late 3-2 win after Steven Gerrard scored the winner from the penalty spot.
Daniel Sturridge and Phillippe Coutinho had twice drawn the Reds level, with Meulensteen left feeling aggrieved that Fulham ended the game empty handed.
"I definitely think we deserved a point," he said.
"If you look at the game, we got our noses in front again. We actually played quite well, were well organised, we didn't let them settle into a rhythm. They didn't cause us too much danger.
"Out of a nothing ball, Gerrard made a pass with the quality he's got and they stuck it in the net so you have to start again.
"We did, we took the chance which fell for us to see us go 2-1, but they came back."
Fulham remain rooted to the foot of the table following the narrow defeat and are four points from safety as Meulensteen rued the late penalty conceded by full-back Sascha Riether.
"What you will see from a team in this position is that they will try to hold on more than build on it," he added.
"So you drop a little bit deeper, get the balls in the right area and stop them hurting you.
"That was the case with the Coutinho goal, letting him come inside and then there was a deflection. Then the third one was just a silly challenge that should not have been made by Sascha."