If you have multiple virtual hosts on your webserver, installing Varnish will cause all virtual hosts to be cached. With VCL it’s possible to exclude some virtual hosts.

sudo nano /etc/varnish/default.vcl
sub vcl_recv {
    # Don't cache domain1.com or domain2.org - optional www
    if (req.http.host ~ "(www\.)?(domain1.com|domain2.org)\.(com|nl|org|dev|local)") {
        return (pass);
    }
}

sub vcl_deliver {
    # You can optionally set a reponse header so it's easier for you to debug if Varnish really didn't cache objects for the host

    # Don't cache domain1.com or domain2.org - optional www
    if (req.http.host ~ "(www\.)?(domain1.com|domain2.org)\.(com|nl|org|dev|local)") {
        set resp.http.X-Cache = "EXCLUDED";
    }
}

After editing, execute:

sudo service varnish restart