The last time Carroll, who is spending a season on loan from Liverpool, had found the net was for England at Euro 2012 in June but his last Premier League goal had come for the Reds in a win over Blackburn in April.
The 23-year-old, who cost Liverpool $35 million, told West Ham's television channel they had to put the Tottenham loss behind them and focus on Wednesday's trip to Manchester United and Sunday's home game against Chelsea.
"It was about time, to be honest," said Carroll of scoring his first goal for West Ham. "I'm just grateful to have got off the mark and hopefully there will be more to come this week.
"I think I've put myself about and been involved in our goals in previous matches. I think I've been doing well so it was about time one went in.
"It was a great ball in by Joey O'Brien and I just had to get up and head it across the keeper. That's what I did and thankfully it went in."
Carroll knows that West Ham, eighth in the league table on 19 points, will have to raise their performance to get anything out of their trip to leaders Manchester United midweek.
After hosting Chelsea on Sunday, West Ham will then have a home game against Carroll's parent club Liverpool to look forward to.
"We have got a tough week, obviously, with Manchester United and then Chelsea and Liverpool coming up. It'll be tough so we just have to put this behind us now and focus on Wednesday.
"Of course, the big games are what everyone looks forward to, but tonight was disappointing and we just have to put it behind us now and get ready for the Manchester United game.
"This game is all gone now so we're going to have to concentrate 100 percent on Wednesday, which is going to be another tough game."
