The hosts started the livelier of the two sides at Craven Cottage with Dimitar Berbatov being presented with two early opportunities.
However, the Bulgarian was unable to convert the chances and Sunderland opened the scoring courtesy of an Adam Johnson free-kick before doubling their tally just before the break as Ki Sung-yueng fired home.
Fulham gained a lifeline shortly after the restart when Steve Sidwell headed home a Damien Duff corner before Johnson inflicted defeat on the hosts as he completed his first Premier League hat-trick.
Meulensteen was left frustrated by his side's opportunities and felt the outcome could have been different, if they had capitalised on their early momentum.
"I think we started really well, we dominated and controlled the game," he told Sky Sports.
"We worked out one or two chances which really you need to take and get your noses in front."
Both of Sunderland's first-half goals came through free-kicks with Johnson scoring directly with the first before executing a fine training ground move to set up Ki on the edge of the box.
Meulensteen admits they knew the threat Sunderland, who have scored eight of their 19 goals from set pieces this term, posed and claims it is disappointing to concede such goals.
"With the free-kick going in you give yourself a very hard task to come back and that task grew only more difficult when they scored the second one," he added.
"They [first two goals] were avoidable because we know the strengths their players have, we know Adam Johnson's set-pieces so you don't give unnecessary fouls away in those areas.
"The second one is a worked free-kick, which we knew they were capable of doing, we addressed it in the team talk and it's very disappointing when a goal like that goes in."
Sidwell's header shortly after the restart gave Fulham hope but Meulensteen admits conceding a third Sunderland goal finished them off.
"I said at half-time, probably a similar thing to when we were two down against City, if you want to get something out of this game, you need to get this next goal," he said.
"If you do you build a momentum and go from there, we did that and we were working our way up, in and around the box but they break from the counter to score and that was the killer blow."
Prior to the weekend Fulham had won two of their last three Premier League outings, moving them out of the relegation zone.
Meulensteen would be forgiven for thinking Sunderland, who came to London bottom of the table, should have been another win under their belt and the Dutch coach insists Fulham must now bounce back.
"It's a big blow," he admitted. "It was a massive opportunity to slide further up the table. We have to take this one on the chin, brush it off and make sure we're better in the next one."