The Cottagers fought back from two goals down at half-time to make it 2-2 after 70 minutes, but substitutes Jesus Navas and James Milner scored two late goals to win it for City.
Yaya Toure and Vincent Kompany had given City a 2-0 half-time lead, before Kieran Richardson and a bizarre Kompany own goal temporarily restored parity.
"I think all the performances have been very positive since I took over," said Meulensteen.
"At half-time we really assured ourselves by saying 'listen, we're sitting here 2-0 down from two set-plays, but making sure that playing-wise we are giving a good account for ourselves, and if we can claw one goal back we can get back into it' and that's what we did.
"We know the sort of quality players that they've got and they can just turn that on, as we know.
"But if you look at the first half, we conceded two goals from set-plays.
"The first one was hard to concede but it was fantastically taken and that's the quality Yaya Toure can produce.
"I think the second one was sloppy from our side, just before half-time, but we did well enough to make sure we certainly stayed in the game."
The Dutchman also praised the experienced players in his side when they pulled it back to 2-2, adding: "It is really where I expect the experienced players to kick in.
"We had a little bit of a similar scenario away to Everton; we get the equaliser, it's 1-1.
"Stabilise yourself, just give yourself a bit of breathing space, knock the ball about and that third chance would have come without a shadow of a doubt because we were positive as much as we could be.
"But then to lose a third goal, which is avoidable, that is very disappointing, it makes all the good work undone."
Adel Taarabt was handed a starting place, his first since November, and provided the assist for Richardson's goal after a marauding run down the left.
"I thought he was magnificent, absolutely brilliant," said Meulensteen of the Moroccan, who played as the lone striker.
"It shows again that sort of talent that he can produce, and I think playing him where we did today suits him in that respect, because he can utilise all his qualities going forward."