The target man, currently on-loan from Liverpool until the end of the season, had not netted at any level since scoring for his country at Euro 2012. But on his ninth appearance for the Hammers since making his temporary switch from Anfield, he grabbed a consolation goal for Sam Allardyce's side to end his barren run.
"It was about time, to be honest," Carroll admitted to the club's official website.
"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."
The West Ham No.8 went on to speak of his disappointment at his side's performance in the defeat at White Hart Lane, which leaves them in eighth place 19 points from 13 games played.
"It was disappointing as we made mistakes for all three of their goals, really," Carroll reflected. "We should have done better, but they have taken their chances and obviously beat us.
"Coming here we were up against a great team and they showed that tonight with the passing, the rhythm and the pace they have got in their team. I have to say we were just disappointed with our mistakes because they cost us."
The Hammers face a daunting upcoming fixture list, with a midweek trip to Manchester United followed by another London derby at the weekend as Chelsea visit Upton Park.