There are typically two reasons why you are an underleveled jungler: slow clears and poor clears.
Slow clears are self-explanatory. You just take a long time to clear the camps. Champions such as Malphite, Nautilus and Zac fall into this catergory. Usually its the utility tanks that are slow clears. They combat this by being very hardy and very capable early on. These junglers don't need level 2 to take a red or blue buff and have the most versatility early on on where they can start their clears. If you make an unpredictable jungle route you may find yourself more at ease playing these champions.
The poor clearing champions are typically assassin style champions. Rengar, Evelynn, Shaco, etc. Shaco is unique in that he has the fastest camp clear in the beginning of the game. An experienced Shaco can actually clear two camps simultaneously and hit level 3 before anyone even hits level 2. He then exploits this window of opportunity with an early gank. Or counter jungles, so he is kind of an exception to this rule. Counter jungling is typically how these style junglers function. They suck at taking hits but excel at dishing out the punishments. So what you want to do is invade after an early clear and steal the enemy jungler's camps. Or you can try and kill them and get the buff that way. Slightly harder to do but more rewarding if you pull it off. You want to put them at a disadvantage for as long as possible. These junglers are for the most experienced jungle players only as it involves a lot of prediction and map awareness. It's a high risk/high reward style of playing. You will be under leveled only if you screw up, otherwise you'll be on par with everyone else and the enemy jungler will be the under leveled one.