The Championship outfit ran out comfortable winners in bitterly cold Hertfordshire, earning only their second win since the end of October.
Manager Rowett believed that a potential banana skin against their National League opponents was avoided.
He said "I think it was a professional job in the end, it was a difficult game with our current form and perhaps not being as confident as we would like to be.
"It's always a difficult place to come, a non-league ground – it's a brilliant setup, you can see the organisation.
"You've got to match the mentality, and hope that your quality shines through. That's how the game panned out.
"We had a tetchy first 10 to 15 minutes, it was a difficult game.
"Once the first goal went in, it was an excellent goal, we settled down. But when it remains at one-nil, it still gives them an opportunity."
The first opportunity fell to the Championship side after five minutes, when an effort from distance by Troy Parrott went wide.
However, it seemed inevitable that the Boreham Wood back line would be breached, and Millwall took the lead on the half-hour mark. Scott Malone fed the ball through to Kenneth Zohore, who slotted home effortlessly.
Boreham Wood created their best chance of the game on 53 minutes, when Matt Rhead put an effort over the bar from less than 10 yards out.
With sixteen minutes of the game remaining, Millwall got the second goal their play threatened. An inswinging corner by Malone found the head of Shaun Hutchinson, who connected powerfully to seemingly seal the tie for the south Londoners.
He said "I felt that we were fortunate to be one-nil down in the first half. Nathan Ashmore deserved the man of the match, he made two or three very good saves.
"We probably should have been two or three down.
"Jake Cooper shouldn't be on the pitch in the second half, but the boys gave their all.
"They came up against a very good outfit, they're a very good side.
"It was always going to be a tough test, I'm bitterly disappointed but very proud of what the boys have achieved."