The former Manchester United striker scored against West Ham United in the 2-1 win at the Boleyn Ground, but will hope to find the net more often.
Welbeck tapped home Alex Oxlade-Chamberlain's cross to help the Gunners move level on points with fourth-placed Southampton, who they play next, as they took six points from their final two games of 2014.
The £16 million signing from Manchester United told Arsenal.com: “I was pleased to get the goal and I’m looking to score many more goals. If I get the opportunity, I’ll try to put them in the back of the net, so I’m a bit disappointed with the one in the second half as well.
“It was a very important game for us going into the Christmas period and we’re delighted to come out with three points.”
It was Welbeck's seventh goal in 20 appearances, which in itself is not a bad return for a striker during his first season at the club.
He was always viewed as a forward with promise during his time at Old Trafford but had yet to show the consistency to prove he was capable of reaching the very top level.
He scored a hat-trick in the Champions League win over Galatasaray in October but he is averaging close to one goal in every five games in the Premier League, which is a ratio that needs to be improved upon in 2015.