The Shrimpers had the better chances at Gigg Lane but goalkeeper Connor Ripley made several fine saves to prevent Powell claiming a fourth straight win since replacing Phil Brown.
That form has lifted Southend up to 14th in Sky Bet League One while Bury edged off the bottom after stretching their unbeaten run to five.
Powell said: “The best chances came our way, we just couldn’t take them. We had a few other chances too, and crosses that flashed across the box.
“Shayon Harrison showed some good touches and had a couple of good efforts, and the more minutes he gets I think the fans will be more pleased with him.
“Fair play to Bury, they’re fighting for their lives and defended heroically as well. They’re very direct and tested us once or twice, but I thought my players stood up to it well.
“On a tricky pitch, when we’ve had a long way to come, I’ve got to be pleased with the attitude and application of the players.
“It’s another point and another clean sheet. The defenders were outstanding. We’ve now had two clean sheets in my first four games so it’s a good start. It keeps us going.”
Ripley denied Michael Kightly and Freddie Ladapo in the first half and the on-loan Middlesbrough keeper was at full stretch to stop a low strike by Southend’s new Tottenham loanee Harrison.
Bury striker James Hanson saw a tame header saved early in the second half while Peter Clarke had a header cleared off the Southend line.
The visitors finished strongly, with Dru Yearwood firing wide before blazing over after Ripley parried a Harrison shot.
And Ben Coker’s late effort from a tight angle was kept out by Ripley to earn Bury a draw, although other results saw them slip 10 points from safety.
Manager Ryan Lowe said: “Both teams huffed and puffed, and I think it was a fair result.
“It was a tired performance from both sides tonight. They’d travelled a long way and we’re scraping the barrel in terms of players.
“We tried to freshen things up as much as we could and had two young lads on the bench. We still felt we could beat them but it wasn’t to be tonight.
“I had a word with them at half-time but it was constructive. The lads took it on board and I thought we were the better team in the second half.
“I’m proud of what the lads have done over the last five games and what we’re trying to achieve – to get the club out of this mess.
“It doesn’t happen overnight but it’s another point, a clean sheet and we’re off the bottom, so it’s another step in the right direction.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.