The visitors scored three own goals to help Liverpool to their biggest win since September 2009, when the Reds beat Hull City by the same scoreline.
The win sets up a home tie with Stoke City in the quarter-finals after Tony Pulis’ side earned a comfortable 2-0 win against Crawley Town.
“It’s a good victory but it was more difficult than the scoreline suggests,” said Dalglish.
“Brighton played very well against us at the AMEX in the League Cup and for half an hour or 40 minutes here they were very good as well.
“We deserved to win and go through but whether the score is a true reflection of how the game went, that’s open to conjecture.
“You can’t blame their boys for wanting to defend their goal, they were just a bit unfortunate.
“Someone said we had 15 attempts on target. We’ve said we’d like to get our conversion rate up and that’s not a bad return.”
Liverpool took an early lead when Steven Gerrard’s corner was met at the near post by Martin Skrtel, who glanced his header past Brighton goalkeeper Peter Brezovan after five minutes.
Despite the home side’s dominance, the Championship outfit levelled in the 17th minute courtesy of Kazenga LuaLua’s stunning free-kick which left Pepe Reina stranded.
But the Reds surged ahead again just before half-time, when Charlie Adam’s corner was headed towards goal by Glen Johnson, and Brighton failed to clear with the ball ricocheting into the net off Liam Bridcutt.
Liverpool’s place in the sixth round was secured after a wonderful move involving Gerrard, Luis Suárez and Stewart Downing, with the winger providing a perfect cross for Andy Carroll to fire past Brezovan.
Own goals from Bridcutt and Lewis Dunk added extra gloss to the scoreline, before Suárez compensated for his 80th-minute penalty miss by adding Liverpool’s sixth.
Dalglish heaped praise on Carroll, Gerrard and Suárez after the trio started their first match together since both strikers moved to the club in January 2011.
“The three of them are fantastic footballers and they played fantastically today,” said Dalglish. “The more any team gets their iconic players on the pitch, the more chance they’ve got of being successful.
“But we’ll stand and be counted as a squad.”
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