It was the Shrimpers' first win in seven games, but Brown said he had felt a victory was just around the corner after seeing positive signs in training.
First-half goals from Conor Clifford and centre half Luke Prosser secured the win, Southend's second on the road this season, and they might have scored more in the second half.
Brown said: "Today was more about keeping a clean sheet than anything else. We were looking to try and get a 1-0 win some time and in the end we got a 2-0, and it should probably have been more, because their keeper's made three one-on-one saves.
"The win's long overdue. We drew parallels with Oxford's league position now and how they started the season because they began by winning the first three games, the same as we did.
"In their next, they got a 2-2 draw with Wycombe with a 94th-minute equaliser and gained great confidence from that, while we lost at Chesterfield to a 96th-minute goal and that seemed to knock us.
"So I thought there wouldn't be much between the teams and there wasn't...except there was with us scoring two goals and we possibly could have had more.
"I thought the wind was just coming back into the sails of the team in training this week."
Clifford's opener came when he hammered in a low shot from 18 yards after a poor defensive clearance by Oxford midfielder Asa Hall.
And Prosser capitalised on a lack of marking to head in Kevan Hurst's deep free-kick on the half hour to put Southend firmly in charge.
Brown added: "It's nice for Conor, he's only a young lad. When he was left out after a couple of games he showed his disappointment, which is natural.
"Today he showed tremendous tenacity to put himself about and I think he must have tackled every single player on the park, and he got a good goal.
"We've felt Luke should have had more goals really, for someone who's 6ft 4in. He celebrated like it was a long time coming. Kevan Hurst's quality delivery was what set that up.
"It wasn't a case of weathering the storm in the second half because we dealt with the pressure that we expected would come, and then had good chances to score more goals.
"I wouldn't say this lifts any pressure, if anything it maybe puts some on. The expectancy level at our club is quite high, and we've showed signs today of what we're capable of."