The Dane smashed home the winning goal from 25 yards out in the 88th minute to keep a top-four finish in the Premier League firmly within Spurs' control.
Mauricio Pochettino's side are third in the table and have three games to play, but only have a four-point cushion over fifth-placed Arsenal, who have a game in hand, while Manchester United are a further two points back in sixth.
With Spurs also preparing for a Champions League semi-final against Ajax, Eriksen wants to ensure his team keep on winning for the remainder of the season.
Speaking after Tuesday’s match, Eriksen said: “Before the season started we would have signed up for being in the semi-finals of the Champions League and being where we are (in the Premier League).
“Of course, we would love to have gone even further in the Premier League as well but at the end you need to win the games you can, we’ve done that in the Champions League and we also need to do that in the Premier League to secure our place in the Champions League again next season.”
After his goal overcame Brighton's stubborn resistance, Eriksen expressed his relief at earning Spurs a valuable three points, saying: "It was relief, yes, unbelievable.
“It was a good strike – I had a few before that! I was warmed up to shoot and very pleased it went in.
“We know these games are very close and very tough. Brighton are a difficult team to play against because they are waiting for us, everyone was in their box so it’s difficult to find any space to play any football and create any big chances.
“We keep going until the last minute. We had chances and that was the case in the other games as well, games where we should have scored before instead of making it so exciting and nerve-wracking! In the end it’s about taking the chances you get.
“This was a one-way game and it’s difficult to break through. It was possession from halfway in their half to the goal, they kept their positional plan and we tried to break through.
“We needed a result – so did they – and it was patience, building and trying to create something out of nothing. In the end it was a big win.”