Why is energy lost here? Let's say a $1 \ \text{kg}$ block is moving.
With a speed of $1 \ \text{m/s}$ so its kinetic energy is $\frac{1}{2} \ \text{J}$. Now let's gently place a block of mass $3 \ \text{kg}$. Now as linear momentum is conserved due to lack of external forces on the system the blocks move together with velocity $1/4 \ \text{m/s}$ but the energy is now $\frac{1}{8} \ \text{J}$ which is lesser than it used to be.
Where has the energy gone?
 A: Energy is lost due to work done by friction . Try to analyze each block individually.
A: "let's gently place a block of mass 3 kg"
Maybe you should rethink the system. You cannot "add stuff" just like this. Energy is conserved in an isolated system. Adding a block just like this is not what I would consider as isolated at all.
Put the two blocks (or one) and then tell us what you want to do.
A: Let the initial body be $A$ and let it move along $X$ axis. Let the other one be $B$
The reason why we get loss of energy is because we are looking at half the picture. Ideally if body $B$ was to fall on to body $A$, then it should bounce back from conservation of momentum (no matter how small the speed of placement was). But some stickiness to the surface is preventing this. So the energy of motion of block $B$ was absorbed by this attractive sticking force. The full story of what happens to the energy and why we generally call this loss a heat loss is there below.
As some answers mention, we cannot add stuff to the system. So a different form of this question is more reasonable.
Imagine a body $A$ moving along $X$ axis over a table (no gravity no friction). Let another mass $B$ be slowly approaching $A$, collides with $A$ and sticks to $A$. This is equivalent to placing the body gently.
where the energy goes
If no stickiness existed, Body $B$ bounces off from $A$ trying to move away but the sticky force pulls it back with all molecules in glue pulling back.
Now a when the molecules of the body and glue attract each other, both molecules would gain speed. the mutual attraction transfers the energy slowly from $B$ into the glue molecules.
This higher speeds would increase the vibration of atoms in the glue, which is equivalent to a rise in temperature. That is why we also call this heat loss
the main take away is that - as feynman says - there is no non-conservative forces. Energy is always conserved but we are lazy to calculate all the energy.
Also to mention this is generally known as a perfectly inelastic collision.
