You were probably overexposing by keeping the shutter for too long. You have to keep eye on the exposure meter and not randomly slow the shutter speed.
In such a situation, first click at the longest exposure you can without over exposing the image and then click some 15-20 images more. Then merge them all in Photoshop/Lightroom to get long exposure equivalence.
For example, I took around 20 images at 1/20 of the seconds and merged them all in PS to get the below effect.
20 images at 1/20 of a second will get out an equivalent exposure of 1sec.
View attachment 724275
Go through this video tutorial, I applied the same technique.
Watch from 2:40 mins for this technique.
Of course, getting a ND filter is an easy way to do it. But till you buy one, you can try this out.