Shaun Batt bagged a brace while David Mooney, Lloyd James and Dean Cox also got in the act for the League One leaders, with Luke George and Matty Flynn registering for the visitors.
Slade made five changes to his regular starting line-up but still saw his side ease through.
"We looked a capable force going forward but I don't think, in parts, that we looked so good when we lost the ball," said the O's boss.
"But the important thing was to get the job done, which we have."
Four players were forced off due to injury in the first half, with the visitors losing three of those and two, including first-choice goalkeeper Danny Hurst, in one incident when they were already two goals down.
"We lost a little bit of momentum from that," Slade continued. "To be fair to Southport it seemed to galvanise them a little bit and they got back into it when they scored form a free-kick but our goal just before half-time put paid to everything to give us a 3-1 interval lead.
"I told my players at the break that they needed to be better without the ball, it's important in these games not to take liberties, you need to be aggressive and ruthless and do things in the right way.
"We showed enough professionalism to make it through, we went through comfortably and it gave some much-needed time on the pitch for some of our squad members to show what they can do because obviously they have a part to play between now and the end of the season."