Matty Fryatt's second-half double proved enough for victory at Roots Hall over former Tigers manager Phil Brown, with Bruce fielding nine changes from the last Barclays Premier League match.
With record signings Nikica Jelavic and Shane Long ineligible, Fryatt and recalled Danny Graham - linked with a move away in the January transfer window - led the attack while goalkeeper Steve Harper came into the side along with the likes of Abdoulaye Faye and David Meyler.
The Premier League team, 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.
Bruce said: "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.
"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."
Bruce feels the competition offers him the chance to fully utilise the squad.
He said: "Somebody like Matty Fryatt, if I don't give him an opportunity to play, then they are knocking down the door.
"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 accepted things could have panned out very differently had the FA Cup weaved its special magic on the south coast once again.
He said: "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.
"We have shown enough resilience and that little bit of quality at the death to make sure the game was ours."
Bruce added: "We are in the last 16 now, which is terrific, so let's look forward to the draw."
Brown - who took Hull to the top flight via the play-off at Wembley in 2008 and kept them up the following season - felt his side could take heart from their efforts.
The Southend manager said: "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.
"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.
"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."