Pochettino's side lead third in the Premier League at Tottenham Hotspur Stadium, but the defender's Brighton limped off in the 88th minute.
Eriksen ultimately completed Brighton's style before the ball came up, leading Tottenham to three points ahead of fourth-placed Chelsea and four ahead of Arsenal.
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"The club is not new as we want, not just legs, but the brain, so we should congratulate the players, and I am proud of them," Pochettino said.
"Brighton were really courageous, the most important thing is to believe, I did not give up."
Although Arsenal can score one point in the table if they win at Wolves on Wednesday, this was an important result for Spurs to qualify for the Champions League next season, in fourth place.
Tottenham have now won all four games in all competitions when they play a new game, scoring eight goals.
This was the biggest disappointment of £ 1 billion ($ 1.3 billion) while the home side said that Harry Kane did not hurt him until Eriksen saved his ninth goal of the campaign in all competitions.
8 goals scored.
The goals are scored.
– Tottenham Hotspur (@SpursOfficial) April 23, 2019
But Pochettino was happy with the way his players faced at the end, despite their influence on their list of candidates.
"There were more than 20 attempts and the prize is huge," he said.
"It's three important points we have in a good position at the table."
Tottenham will take another step to ensure four matches of the four derby derby at West Ham ahead of their Champions League semi-final tie with Ajax next week.
"We have to be confident, the team is making a fantastic effort after a difficult game against Manchester City," Pochettino added.
The final was a painful Brighton, who have only won two of their last 15 league games and sit just one place and three points above the relegation zone.
They failed to score in their last 7 games in all competitions, and are a serious threat to Cardiff to take third place in the battle to avoid looga to leave.
Arsenal and Manchester United's defeat, with a draw at Burnley, Tottenham have come closer to the 1-0 defeat to Manchester City on Saturday.
"We have offered a lot of fighting and a great deal of trust in the last two games.
– Brighton & Hove Albion ⚽️ (@OfficialBHAFC) April 23, 2019
While Brighton is defending, Lucas Moura is close to Dele Alli, but Lewis Dunk has hit out at the end of the game.
Going to Pochettino is likely to bring Fernando Llorente to his biggest stride to force his son Heung to play alongside South Korea in the middle of the middle of the week.
The first half of the match was scored by an unbeaten goal,
Spurs denied Brighton's defense for the first time in possession of a six-match ball in the Alliance, and only scored for Shane Duffy.
Duffy was threatening at the end of the game when his head was forced by Tottenham goalkeeper Hugo Lloris to start the game for the first time in the second half.
Danny Rose, 20, was well saved by Mat Ryan, while Lucy Alderweireld's luck was also lucky after the Tottenham defensive midfielder slammed his left hamstring and his left foot.
Pochettino is hopeful that striker Vincent Janssen made his debut for 20 months.
Janssen did not make much of a penalty but Tottenham put the equalizer in the 29th minute when Eriksen struck in the 88th minute.
Gooldhigiisii 25-yard between, midfielder of Denmark's attack on Ryan's left leg welcome place, scoring a victory celebration.