Parkinson's men guaranteed themselves a top-five finish in the regular league season with a game to spare thanks to Lee Evans' twelfth-minute winner at Roots Hall.
The Southend victory ensures City will now have at least two further games to add to their calendar ahead next Sunday's final match of the normal campaign at home to Chesterfield.
Parkinson said: "We didn't want to go into the last game of the season looking over our shoulder.
"We have achieved our aim of getting into the Play-Offs. We're delighted with that, and it is a fantastic achievement for everyone connected with the football club.
"We take a deep breath now, enjoy this feeling tonight, and then get ready for an exciting set of games for us.
"We have worked hard to get there (the Play-Offs) and we are going to relish every moment.
"I'm pleased for Evo (Lee Evans) - he has been going close in recent games.
"He has great technique and you know if he keeps hitting the target one would go in for him.
"Southend threw everything at us in the second half but we dealt with it so well.
"We had chances ourselves to extend our lead but we just couldn't get that second goal.
"We played intelligently though, all the basics in our game were in place today (Saturday) to get the clean sheet and the win."
Despite the long distance between Bradford and Southend, City were backed by nearly 1,600 supporters at Roots Hall.
Parkinson added: "Seeing the town full of Bradford fans driving into the ground was a great sight for the lads on the coach.
"The momentum is building - they really are our twelfth man.
"It was important that we sent our fans back up the motorway in good spirits and we've managed to do that. I thank every single one of them for coming down to support us today.
"We are all looking forward to the next part of this journey."
Along with the important win, City fans were also able to enjoy the return of Paul Anderson after the winger made an appearance as a second half sub - his first outing in the league since breaking his leg back in September.
Anderson nearly capped off his return display in perfect fashion when he clipped the bar with a looping drive from outside the area in injury time.
Parkinson added: "He is a class player, he has real quality in that final third. He showed that with his effort that hit the crossbar.
"This time last year, Paul was involved in the Championship Play-Offs with Ipswich Town so he has real experience and know-how. He also has that quality to produce that final ball or that finish and it is great to have him back."