use is evaluated at compile time, which eval can't catch. There are a few ways around this:

# Option 1 - string eval, test $@
eval "use HTTP::Request::Common";
if ($@) {
    # Missing
}


# Option 2 - string eval with return value of 1

if (eval "use HTTP::Request::Common; 1;") {
    # Loaded, good
}
else {
    # Missing
}


# Option 3 - require and import

eval {
  require HTTP::Request::Common;
  HTTP::Request::Common->import;
};
if ($@) {
    # Not found
}
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If I recall correctly option #2 is preferred.