"We are working, but we need the results to show in our play, because things are going to come around quickly with the (international) break and the World Cup."
The Qatari-backed club are now top of Group H on goals scored above Benfica, who won 2-1 at Juventus.
Haifa threatened a shaky PSG defence throughout the game, but the Ligue 1 giants passed the test thanks to their front three.
"The fact that the three of us can make the difference in a game is an advantage for us," Mbappe added.
"I hope that all three of us keep scoring as it means that we'll win matches."
Paris, still searching for a maiden Champions League title, go into home and away matches against Benfica knowing that two wins would secure a place in the knock-out stage.
PSG could have taken the lead inside 70 seconds as Mbappe burst into the box, only to see his effort denied by a sprawling save from home goalkeeper Josh Cohen.
Mbappe spurned another excellent chance as he got in behind the Haifa defence again but took a heavy touch.
Haifa take shock lead
The Israelis grew into the game and took a shock 24th-minute lead as Dolev Haziza was given time and space to whip in a cross which was volleyed home by Suriname international Chery.
Haifa briefly thought they had scored again when Frantzdy Pierrot put the ball in the net, but the flag was raised for offside.
PSG dragged themselves level eight minutes before the break, as Mbappe's low cross was deflected perfectly to Messi who slotted the ball past Cohen from close range.
Haifa kept pushing for a deserved half-time advantage, but Omer Atzili dragged a shot wide and visiting 'keeper Gianluigi Donnarumma made a flying save to tip away Chery's long-range strike.
PSG continued to struggle at the start of the second period, but gradually improved and Messi forced Cohen into an excellent low stop in the 65th minute.
The French champions forged ahead for the first time four minutes later, as Messi slipped a pass through for Mbappe to slide a shot into the far corner.
Haifa kept pushing for an equaliser, but just seconds after Chery blazed a free-kick over, PSG countered and Neymar fired the ball into the bottom corner to complete the scoring.