Goals in each half from Matty Cash and Ollie Watkins earned them a 2-0 victory on the south coast, to ease fears of being dragged into a relegation battle.
Gerrard saluted the composure of his players on a difficult day which saw their journey to the Amex Stadium delayed by heavy traffic and kick-off put back by half-an-hour.
He said: “It is always important when you are going through a sticky patch that you stay together and keep believing in the right things.
“It is only a matter of time before it changes. The important thing for us is to take the confidence and belief from today’s game and build on it next week against Southampton.
“The preparations were challenging today because of the delay but the players remained focused.
“The most pleasing thing for me was the way we controlled the game out of possession.
“I thought we were really organised, everyone really brought into what we were looking for and that gave us a really good base to win.”
Gerrard, meanwhile, took responsibility for the booking picked up by Cash after his 17th minute opener.
The right-back removed his shirt to reveal a message of support to Poland international team-mate and Dynamo Kyiv defender Tomasz Kedziora, who is currently in Ukraine.
“I will take responsibility for Cashy’s yellow card,” said Gerrard. “I should have spoken to the players before the game and said: ‘Listen, if we score any goals let’s remain calm’.
“We all have to respect the situation and that is what Matty was trying to do. I will take responsibility toward that. There is no blame toward Matty. Everyone is trying to understand the situation. That one is on me, not Matty.
“I think the Premier League have taken things into account. The yellow card is on us. Maybe because of our late arrival we did not get it too clear to the players.”