Python 2, 101 bytes

2 bytes thanks to @xnor.

import os
t=-1
for n in range(input(),input()+1):
 if~-os.path.isfile(str(n)):
  if~t+n:print n
  t=n

Dyalog APL, 25 24 or 36 bytes

Prompts for lower bound, then upper bound.

It seems from comments to other answers that the OP wanted as short sequences as possible.

{⍵/⍨~⍵∊⍨⍵-1}((⍳⎕)~⍳⎕-1)~⍎¨⎕SH'dir/b'

{
    ⍵/⍨ those where it is
    ~ not true
    ⍵∊⍨ that the set contains
    ⍵-1 their predecessor
} of
(
    (⍳⎕) of the integers until n
    ~ except
    ⍳⎕-1 integers until n-1
)~ except
⍎¨ the evaluation of each of
⎕SH'dir/b' the bare list of names in the current directory

Old answer which returns length-1 sequences:

(⍕¨(⍳⎕)~⍳⎕-1)~⎕SH'dir/b'

(
    ⍕ string representation
    ¨ of each
    (⍳⎕) of the integers until n
    ~ except
    ⍳⎕-1 integers until n-1
)~ except
⎕SH'dir/b' the bare list of files in current directory

Only works on Windows. A cross platform solution:

(⍕¨(⍳⎕)~⍳⎕-1)~0⎕NINFO⍠1⊢'*'

0 just the filename(s)
⎕NINFO of the Native file(s) INFOrmation
⍠1 using wildcards
⊢'*' on all files

Perl 6, 49 bytes

{my $c;.say if .IO.e??($c=0)!!!$c++ for $^a..$^b}

Tried to use flipflops. Didn't manage to :P.

Ruby, 74 60 bytes

Input is in command line, run it like ruby f.rb 0 20. Only works in current directory.

-1 byte from unpacking the ARGV into variables, and -13 bytes from replacing the select and grep with a set subtraction.

a,b=$*
f=[*a..b]-Dir.glob(?*)
puts f-f.map{|e|"#{e.to_i+1}"}

PHP, 64 bytes

<?=implode("\n",array_diff(range($argv[1],$argv[2]),glob("*")));

Run like this:

php -f golf.php 1 20

Note:

• Only does the current directory.

• No trailing newline on the output.

• This requires the <?= to be allowed in php.ini. Which I think is default but I'm not sure.

Bash, 31 bytes

a(){(seq $@;ls)|sort|uniq -u;}

Run as a 1 20. Again, only does the current dir.

Can I submit two? Hope so. This is my first post to Code Golf so I'm not too sure of the etiquette. Hope I'm counting my bytes correctly, too.

PowerShell v4+, 62 bytes

param($x,$y)$x..$y|?{$_-notin($a=(ls ".\").Name)-and$_-1-in$a}

Save as a script in the desired directory and call it locally (see example below). Takes input $x and $y and constructs a range .., then pipes that to a Where-Object (the |?{...}) which is basically a filter. Here we're only selecting items where the current element $_ is -notin the .Name collection of the current directory, but the previous element is -in that collection (i.e., only the start of a missing range).

The ls is an alias for Get-ChildItem and is basically what you'd expect. Requires v4 for the encapsulation-select of .Name, otherwise you'd need $a=ls ".\"|select Name.

Example

PS C:\Tools\Scripts\golfing\misd> ls .\

    Directory: C:\Tools\Scripts\golfing\misd

Mode                LastWriteTime     Length Name
----                -------------     ------ ----
-a---         7/26/2016   7:48 AM          8 1
-a---         7/26/2016   7:48 AM         10 10
-a---         7/26/2016   7:54 AM          0 18
-a---         7/26/2016   7:48 AM          8 2
-a---         7/26/2016   7:48 AM          8 3
-a---         7/26/2016   7:48 AM          8 4
-a---         7/26/2016   7:48 AM         10 7
-a---         7/26/2016   7:48 AM          8 8
-a---         7/26/2016   7:48 AM          8 9
-a---         7/26/2016   8:18 AM        365 misd.ps1

PS C:\Tools\Scripts\golfing\misd> .\misd.ps1 1 20
5
11
19