The Tigers' bonus-point win in front of their own fans at Welford Road left them in third place, just five points behind Northampton. The title is decided by play-offs involving the top four at the end of the regular season.
"It was a good win, but we can still do some things better as well," said Parling after a victory featuring two tries from hooker Jamie Blamire.
"I was really pleased with our edge. We were on a real sweet spot physically and I'm also pleased we managed to stop them scoring a bonus point."
Nevertheless, 42-year-old former England lock Parling, twice a Prem champion with Leicester as a player, added: "But we also know what still lies ahead of us. We've got three really important games left in the regular season, starting with Sale away."
Had Northampton scored a bonus-point win they would have qualified for the play-offs and Saints boss Phil Dowson made no attempt to minimise the impact of defeat in the East Midlands derby.
"It was very painful," he said, adding: "I hope we take the scars and take the lessons out of it and stay together. We now need to work incredibly hard in preparation for Bristol at the (Franklin's) Gardens on Friday night."
In Saturday's other Prem match, Saracens survived two late yellow cards to keep alive their play-off hopes with a 41-26 win at Bristol.
Their bonus-point win saw sixth-placed Saracens cut the gap to Exeter and Bristol, who both remain just above the London club, to two points.