$ perl -Mstrict -Mwarnings -E 'while (<>) { if (/my background error (\d+):(?!.+my3\.exe)/ ) { say $1 } }'
blah blah my background error 1234: blah blah
1234
blah blah my background error 1234: blah blah my3.exe blah
blah blah my background error 1234: blah blah my4.exe blah
1234
blah blah my background error 1234: my3.exe
blah blah my background error 1234:my3.exe
1234
^C