I think generally it's hard to "fake" being behind because your board state is your board state. Unless you have something giving all your stuff flash or something, in most cases it doesn't really matter if you have an Ulamog in hand and castable if on board you only have a vanilla 2/2 and the green player has an army of 12/12 tramplers. If you have lands in hand, for instance, you're generally better off playing them than holding back to hope that "oh, I'm so mana screwed" gets you further later.

On the other hand, there's also playing smart. If you know there's a boardwipe coming you probably want to hold on to your creatures. I try not to play turn 1 sol ring, even if I draw it, because that makes all eyes turn to you and any big thing that you might drop as a result of that will be coming out when everyone else is most likely to have some kind of removal, and often when there's nothing better to spend mana on. If a player is sitting on two untapped blue mana what are the odds that he's sitting on a counterspell? Can you bait out the counterspell with a threat now so you're able to do what you really want later? Or hold off casting in the hopes that it gets dropped elsewhere?

@TheMagicer I guess it depends on what you mean by "fake falling behind".
I do conserve my resources to avoid being perceived as a threat. That's not only proper resource logistics, it's also saving my stuff from removal to reduce risk.
I will also argue that I am not a threat based on my board state compared to other players, or try to convince people that some plays are unnecessary.

I think the difference is between lying about my luck vs being strategic in how I present my board state

Won me a tournament by pretending I flooded. Playing greven, I had 3 of my win on the spot pieces and 3 lands (mulled once down to 6). Drew 3 lands and my final piece, but vocally complained about flooding. Only player playing blue tapped out on turn 5 so I went all in an knocked him out. Rest of the table conceded as I had managed to reset my health and draw 20 cards. Greven is love.