The Reds captain, whose side beat Pompey 4-1, seemed to aim an elbow at Brown's head in the 73rd minute and was substituted immediately afterwards.
Referee Stuart Attwell gave a foul but may be asked to assess the match video.
Last week at Wigan, Gerrard escaped punishment after appearing to flash a V-sign at referee Andre Marriner.
However, Liverpool boss Rafael Benitez does not believe England midfielder Gerrard will face repercussions from the clash with Brown, either.
"I don't think so," said the Spaniard when asked if he was worried about retrospective action against Gerrard.
"I haven't seen it but I was asking and I think it was nothing."
Liverpool led 3-0 when Gerrard was taken off but Benitez insisted the substitution was not because of the incident and stated: "We were thinking of changing Fernando Torres, Glen Johnson and Gerrard and we did it."
Attwell awarded Portsmouth a free-kick over the incident but did not book Gerrard.
Portsmouth manager Avram Grant also did not see the coming together of the two players.
"They told me the ref was four metres away so I think he needs to see from four metres what I didn't from 40 metres," said Grant.
The spat slightly overshadowed a fine Liverpool victory - one that reignites their push for a top-four finish this season.
The victory - only their second win in five league matches - takes the Reds above Manchester City into fifth spot and right back in the hunt for fourth place and Champions League qualification.
"I think it was a good game - we played well, scored four goals and I was pleased with the players," added Benitez. "The confidence was there and we looked like we could score at any moment.
"It was important to win this game and it will be important to win every game now until the end of the season."
It was the perfect start to a big week for Liverpool, with the Reds set to face Lille in the second leg of their last-16 Europa League tie on Thursday and then facing Manchester United at Old Trafford in the Premier League on Sunday.
Benitez believes his side, who must overturn a 1-0 first-leg deficit against Lille, can win both games.
"The week has started really well so hopefully we can win on Thursday and win on Sunday," he commented. "I have confidence we can do that."
Meanwhile, Portsmouth boss Grant paid tribute to his side's character, despite their crushing defeat, and assured supporters he would not allow the players to give up in the face of their near inevitable relegation.
"Every player - even those who did not play so well tonight - showed good spirit and we could have scored before we got our late goal," said Grant, whose side are bottom of the table.
"We did OK until the first goal and then we conceded three very quick goals and it was very difficult after that, of course.
"It's very difficult to keep the players going, very difficult, but we have shown before that we can do and we will continue to do it.
"I don't want us to give up, I don't want us to surrender - we will fight and we will see what happens."
Source: BBC Sport