Matty Fryatt's second-half double proved enough for victory at a wet and windy Roots Hall over former Tigers boss Phil Brown, with Bruce fielding nine changes from the last Premier League outing, which they lost to Norwich City.
The Premier League side, though, had more than enough quality to see them through, with the Shrimpers - going well in the promotion race - restricted to a few chances, although things could have been different at the start of the second half when a 30-yard strike from Michael Timlin crashed against the crossbar.
Hull eventually made the breakthrough on 62 minutes when Fryatt latched on to a loose ball in a crowded box to drive a low effort into the bottom right corner.
The Hull forward made sure of progress when he cracked home a second in stoppage time after collecting a ball down the right and cutting in at the near post.
"I would not expect a team of mine to roll over just because we are coming here in the cup, so they showed the right desire and attitude," Bruce said.
"The pitch was difficult, and towards the end it was awful conditions, a typical cup tie, sometimes in football you have to roll up your sleeves and we did that in abundance today to get through."
With an important trip to Selhurst Park to face Crystal Palace in the Premier League on Tuesday, Bruce utilised the cup tie to test the depth in his squad and was delighted with the results of his experiment.
"Somebody like Matty Fryatt, if I don't give him an opportunity to play, then they are knocking down the door," he added.
"Matty had come back into the side today and reminded me what a good player he is.
"I was confident we could come here and make the changes, they are all experienced players - Abdoulaye Faye, [Paul] McShane, Meyler, [Stephen] Quinn, [George] Boyd, Matty Fryatt, Danny Graham, and we should be good enough if we do it right to get through and I had big belief we would do that."
Bruce admits with the media hovering in search of a cup upset, Roots Hall could have been a banana-skin for the Premier League club but the manager conceded his relief at seeing the Tigers progress.
"We knew with all the cameramen here, radio, it is a shame it was not on the TV because it had all the ingredients of an upset, but fortunately for us we have made sure that did not happen," he added.
"We have shown enough resilience and that little bit of quality at the death to make sure the game was ours.
"We are in the last 16 now, which is terrific, so let's look forward to the draw."
Southend manager Phil Brown, who took Hull to the top flight for the first time in their 104-year history in 2008, believes his side must take heart from their efforts against Premier League opposition.
"I am proud of them, but just disappointed that in the final third was a difference between the two teams, which is where Hull showed a lot of quality," he said in the aftermath of the cup defeat.
"We just did not have that belief and that comes from the exposure to Premier League football and the depth they have.
"With a bit of luck, we could have caused a bit of an upset, and the first goal was so important, their keeper made a vital save in the first half, then we hit the bar and soon after, we are behind."
Brown admits luck was not on Southend's side today but insist they must dust down quickly, ready for a Tuesday night trip to Victoria Road to face Dagenham & Redbridge in League 2.
"It just did not fall for us today, but we can draw a lot from the game and our challenge is now to get out of this division, which means taking on Dagenham & Redbridge on Tuesday night," he added.