Hi Borah and welcome to the forum.
You are quite right you have to see that there is no space left between the last three pearls, you are doing quite right, making simple overhand knots. You keep it tight together by putting your finger behind the 4 pearl from the end (this one has a knot and sits "tight", then you just see to it that you are pushing the 3 final pearls tight against it, adjusting the thread by pulling. Once you have gone back through the first pearl (all the time adjusting the thread so it is close/tight to the pearl), you can put the bracelet down on the table, form the upper part of an "8", go through with your needle, pull the thread/s through so they go tight into the pearl and continue. BTW I always work with double threads. I hope you understand what I am trying to explain...