DIY LED lamp is less powerful than expected
Your connecting wires are too thin, you are dropping voltage in your leads.

You need to select the right size of wire and potentially use a star connection to drive the strings.

If your strip is using SMD2835 LEDs these will be FULLY bright at 12V DC. The typical LED characteristics (when warmed up) will be as below:



Notice that the Vf is around 3.3V maximum and you will find you strip has three LEDs in series with each current limiting resistor. The LEDs visibly turn on at about 9-9.1V (low brightness). If there were 4 in series you would have to use above 12V DC to get them to turn on, and this is NOT the case. 

To select your wire size. there are plenty of charts and in the one shown below you would not use less than 16AWG wire for you application:


The leads from your power supply MUST be able to carry the full current rating. The leads from LED string to LED string could be much smaller if you used a star connection for your wiring.

Most LED strings actually have the voltage marked clearly on the strip, here is one image:


NOTE: The vast majority of LED strings will NOT work in automotive use as they get too hot.