The Saints had two golden opportunities spurned by striker Sadio Mane in injury time.
The acting boss said: "We had some big chances in the last 10 minutes but you have to score to win games so it is mixed feelings that we have.
"It is not a bad start but if you are professional and you get the chance to win you have to win. Ten minutes before the end I thought okay, we are happy with a point, but if you see the last 10 minutes then we have to be disappointed."