Yes, if you don't make the jump you will fall into the alley.
In order to make the jump you must look slighty up, or Jack will fall. All jumps need to be done this way. Jack is also afraid of heights, so looking down over any kind of drop is usually not a good option unless you have no choice.
Don't be sorry. This is a really hard segment for so early in the game. It took all of us completely by surprise!
But you actually made it through the hardest part of the sequence. The rest is a little less intimidating, although those fishmen keep coming after you.