One should first understand the cause and purpose for the executions to have insight into the effect it had on the animals.
The animals were slaughtered because they had confessed to having committed ultimate acts of betrayal against the general purpose of their cause. They had fought bitterly and hard to be free of a tyrannical master and would therefore sacrifice as much as they could to maintain their new-found freedom. When it was declared by Napoleon, specifically through Squealer, that Snowball, who had been banished, had been plotting the overthrow of the farm, there had been a general outcry against his malicious treason.
When some of the animals therefore confessed their complicity with Snowball, they were executed. Other animals confessed to similar acts of betrayal and were also extinguished. The purpose was to ensure the removal of any threat against the farm and ensure not only its survival, but more importantly, that of its leader, Napoleon, and his acolytes.
After the executions, the animals were all shaken and dismayed for they could not decide which was more terrible, the executions themselves or the treason of their previous comrades. They remembered that in the past, under Jones' rule, animals were slaughtered, but ever since his expulsion, not a single creature had been killed. The slaughter now seemed much worse than it had ever been in the past, since they had been killed by their own kind, not by a despotic human.
The animals were clearly traumatised and felt cold. They huddled together to find warmth. They were driven to silence. Only Boxer commented that the reason for this cruel act of retribution must be that they were at fault. In his naïve and simple judgment, he promised to work harder and would rise earlier in the morning. He then left to continue working.
Clover was most acutely affected by the slayings. She was tearful and reasoned that they had all worked so hard for things to become what they had. She felt pain and sorrow for she believed that killing each other was not what they had fought for. Clover's introspection informs that she would follow Napoleon's rule, work hard, follow orders and be faithful in spite of the fact that their lives had become so pitiless.
It is clear that she resented the fact that they could not speak their minds and were continuously watched over by Napoleon's terrible dogs and had to witness such terrible slaughter. Clover was not rebellious at this point - she had clearly accepted her destiny. It seems that this was the general nature of the other animals' thinking as well.
The animals were overwhelmed with a sense of sadness and sorrow and began to sing 'Beasts of England' as if it were a hymn, only to be told later, by Squealer, that Napoleon had banished the song and that it had become forbidden to sing it.
These events illustrate that Napoleon had reached a point where his control had not only become dictatorial, but tyrannical. He would suppress through bloody violence any form of dissent and the animals were, as a result, cowed into submission and had to bow to his absolute authority.
It set fear into the other animals. It was a way of warning them and keeping them from rebelling, as a result the animals took in the warning loud and clear and no one dared to stand up against the pigs, leading them to be imprisoned in their own fear. The animals were also confused by the series of events, Boxer even blames himself/other animals for the turn of event, and thinks the animals have done something wrong to cause such executions. He resolves to work harder, and in turn the other animals seem to follow suit.