Amid talk of a potential push for the top four and Champions League qualification – or even a potential title bid – Welbeck, 32, said the focus is on the ‘most important’ next game.
“We have an historic first game in Europe on Thursday,” the striker told BBC Sport.
"It is going to be a long season. We have a big squad with incredible players and everyone will play their part.
"It is not worth looking too far ahead. Only after Christmas can you start making targets."
Welbeck was speaking after scoring in the 3-1 win at Old Trafford – Albion’s third successive league win over Manchester United.
It was the fourth league goal he has scored against his boyhood club – the most of any player to have previously played for the Red Devils in the competition.
Asked by Match of the Day if he will get some stick from family and friends as a result, he said: “I’ve seen a few in the stands – United fans, friends and family but I’m here to be professional, do my job and I did that today. Got three points and that’s the most important thing.
"Everywhere we go we want those three points, home or away. If we set up well we can get the win. We did that today and played really well.”
Welbeck told the BBC that he had a ‘tough period’ at Watford after leaving Arsenal but now feels at home in Sussex.
"The club environment was not as good as it is at Brighton for me personally,” he said. “I was also coming back from a serious injury.
"We have a great set of lads. We fight for each other every day and it shows on the pitch. We are a team that does the basics with quality on top.
"The way the gaffer sets up the team is just brilliant.”
Returning the complement, De Zerbi said he is ‘not surprised’ by Welbeck’s performances for the club.
The Italian manager said: "I know very well, Danny is an incredible player. He is in one of his best moments in his time in Brighton. He’s playing like a younger player.”
“The qualities of Welbeck are many. Because he can play like number nine, like a striker, but like number 10, because he understands play, understands the the timing, the right position in the right moment. He's a very smart player.”