The 20-year-old centre-back, who signed from Sporting Lisbon this summer, surprised everyone when he broke the defensive line and rounded the keeper to give 10-man Spurs victory at the death on the opening day at Upton Park.
The England Under-21 international told Sky Sports: “I'd have been happy with just the clean sheet to be honest.
"I wasn’t expecting to get up the other end and score and I haven’t scored many goals. I would like to score more so I’m really happy.
“I don’t know what I was doing there. Andros Townsend went outside so I just thought I'd make a run inside and it just happened to fall for me."
Tottenham, under new head coach Mauricio Pochettino, fell a man down early in the game when right-back Kyle Naughton was shown a straight red card after being deemed to have prevented an obvious goalscoring opportunity when he handballed at close range from Kevin Nolan’s shot.
The away side sustained long periods of Hammers pressure but James Collins was dismissed midway through the second half for a second bookable offence.
“We knew it would be a hard place to come and play, they play very direct and play it well,” Dier said.
“We knew it would be hard but with 10 men versus 11 it was even harder, but we stuck in there and got something from the game.
“It’s early days yet though – that was just the first game, so we need to keep going, get our heads down and keep working hard.”