Supporters of the failed legislation said they were more disappointed than angry about the vote, the Pew Research Center reported.
The poll some 32 percent were "disappointed," while 15 percent characterized themselves as "angry" about the result.
Some 20 percent said they were "very happy," and 19 percent said they were "relieved."
The poll's findings reflected a partisan split on the issue of gun control measures such as background checks.
Some 52 percent of Republicans said they were either very happy or relieved the legislation was voted down, while 67 percent of Democrats harbored negative feelings.
Those who had the strongest feelings, pro or con, about the vote were people who had closely followed debate about the gun control proposals, Pew said.
The poll's results parallel findings of a Pew survey in February in which 50 percent of respondents said they favored gun control, while 46 percent favored gun rights.
However, the same poll found 83 percent of those surveyed favored background checks for guns sales between two private parties and at gun shoes.
The poll of 1,002 adults was conducted April 18-21. The margin of error was calculated at 3.7 percent and 7.6 percent, depending on the groups surveyed.