Gavin Tomlin and then Britt Assombalonga gave former Hull boss Phil Brown the perfect start to life with his new club but Zavon Hines's strike and then James Hanson's late header earned the Bantams a point.
"We gave ourselves a lot to do after giving them two soft goals," Parkinson said. "I thought we played some excellent stuff in the second half and ought to have won the game in the end."
Parkinson said he could not understand why Hines' 51st-minute effort that flew into the net was disallowed and thought Bradford ought to have had a penalty when Kyel Reid was brought down only to be booked by Staffordshire referee Steven Rushton for diving.
He said: "You cannot blame the crowd for being frustrated at half time, but we came out in the second half and played with conviction and I thought our three substitutes gave us that extra bit of quality. The lads were excellent - they ran themselves into the ground.
"We dominated the game, but we knew Southend were going to come here with renewed appetite with a new manager and it was a good point in the end after being 2-0 down.
"Now we go to Torquay on Monday and if we can win there this will be a good point, but we have to make sure we don't give the opposition soft goals. We have got to be stronger in those situations."