Boro bossed the first half, creating almost all of the opportunities and went in front after 26 minutes through Stacy Long.
But Barry Corr`s goal six minutes from time earned a point for the Shrimpers.
Westley said: "Southend frustrated us at times and this is the result.
"We needed to be a little more clinical but things didn't quite happen for us in front of goal as well as I'd have liked.
"Southend were always going to be difficult to crack despite their recent run, but we really ought to have pressed more and grabbed the initiative when we needed to."
Source: PA
Source: PA