Glenn Murray has called on Albion to keep their feet on the ground after Saturday's 4-1 win over Swansea.
Murray netted a double to move on to 12 goals for the season, with ten of those in the Premier League, as Brighton ran out comfortable victors.
The striker has now netted five goals in his last five games and moved up to fifth in Albion's all-time top-scorer list with 91 as he overtook Albert Mundy and Bobby Zamora, who both netted 90 for the club.
Saturday's win lifted the Seagulls up to 12th in the table and four points clear of the relegation zone, with ten league matches to play.
Murray scored the opener from the penalty spot, after he was fouled by Mike van der Hoorn, on 18 minutes and then made it 2-0 from Jose Izquierdo's low cross after 69 minutes.
Anthony Knockaert got the third four minutes later, before Tammy Abraham's low shot deflected in off Albion defender Lewis Dunk to make it 3-1 on 85 minutes.
There was still time for club record signing Jurgen Locadia to score his second goal in as many games when he turned home Dale Stephens' low centre in the final minute.
The win extended Brighton's unbeaten run to six matches and Murray admitted it was a huge three points.
He said: "We knew going into the game that if we got three points it would be vital for our task to stay in the Premier League - thankfully we got that.
“The longer the Premier League has gone on, the more we’ve believed in ourselves. There was a lot of us that hadn’t graced the Premier League before this season and the belief has grown throughout the squad.
"But we've got to keep our feet on the ground. As soon as we start speaking about safety and things like that, it's where we could come amiss.
"We'll do exactly as we did last week leading into the Arsenal game and hopefully that will bring some points next week."
Murray added Albion need to continue to pick up points to stay in the top flight, with Arsenal the visitors to the Amex on Sunday (1.30pm). He said: "The league tells you a little bit of a lie really as we're sitting 12th, which sounds great but once you look into it, it doesn't look so great.
"The further we can put between us and the relegation zone, the better for us and at the minute it's not enough.
"Any points we can pick up against the so-called big boys is a bonus and when we play teams in and around us, it's important not to lose so they can't gain ground on us."
Murray admitted a bit of studying paid off after scoring from the spot against Swansea, shooting straight down the middle as Swans goalkeeper Lukas Fabianski dived to his left.
He said: "People think you just step up and pick a side or pick where you're going but we look at the videos. I study each goalkeeper before we play to see what his habits are and what may work against him.
"I'd watched his previous 20 penalties, so I had some idea and thankfully it came off."
Reflecting on the game, Murray felt Albion took advantage when Swansea changed personnel and switched to 4-4-2, having started with a 5-4-1 formation.
He said: "I don't think either team really took the game by the scruff of the neck but we got a penalty and managed to edge in front.
"I think Swansea had the better of the first half after that and second half we came out, got our foot on the ball and Swansea changed their shape. After that we found we had a lot more space going forward and managed to capitalise on that."
Keep up with all the top football news and transfer gossip from England, Scotland and beyond with footballwire.co.uk