Welbeck came on as a substitute in England’s 2-0 win over Costa Rica in an international friendly at Elland Road on Thursday.
The 27-year-old scored in the 76th minute, making it his 16th goal in 39 games played for England, three more than any other player in their World Cup squad.
Speaking on whether he should be given a starting role by manager Gareth Southgate, Welbeck said: “I have played better in games this season for my club [Arsenal] and not scored a goal, but I did score tonight [against Costa Rica].
“I am always hungry for more. I am really excited for the upcoming weeks.
“I have got a good record when I am playing for England, scoring goals, getting into dangerous positions, players have been finding me in dangerous positions as well. I am making runs and always trying to put the ball into the back of the net.
“Tonight there was two up front, Marcus [Rashford] and Vards [Jamie Vardy], and Marcus scored an incredible goal and Vards was dangerous throughout the whole game.
“There is a lot of competition throughout the whole squad and there is a lot of talented players on the pitch. But I think that ups everyone’s game, and it is healthy competition.”
Rashford opened the scoring in the 13th minute, in a game England dominated, and started up front alongside Vardy.
The 20-year-old was named man of the match, leaving Southgate with a decision over whether to start the Manchester United player for their opener against Tunisia in a Group G match on June 18.
Southgate handed an international debut to Trent Alexander-Arnold. The 19-year-old gained a call-up to the squad following an impressive season for Liverpool.
When asked what advice his manager gave him he said: “He told me to keep it simple and play like I do at my club, to not overthink things and I got a text from James Milner as well which was a nice touch from him.
“I really appreciated that, he told me to just go out there and enjoy it, that’s what I tried to do.”