Despite opening the new campaign with back-to-back defeats to Brighton & Hove Albion and Brentford, Ten Hag's team are up to fifth in the table, but the Dutchman insisted it was too early to consider them title challengers.
"We're at the start of a process, we're still far away," Ten Hag said at a news conference. "We have to start doing things much better than we do, that's an investment. We have to get better if you want to win trophies in the end."
Antony scored on his debut following his €100 million move from Ajax, while Rashford scored twice in nine minutes in the second half to move onto three goals for the season -- just two short of his tally for the whole of last season.
"They both played great, a continual threat," Ten Hag said. "I know our offence is really strong -- they are creative and have speed. This is the first time they have played together and this performance is great to see."
Arsenal manager Mikel Arteta, meanwhile, was left to rue a decision by Paul Tierney to rule out an early goal from Gabriel Martinelli after VAR Lee Mason had encouraged the referee to take a second look on the monitor. Martin Odegaard was punished for a challenge on Christian Eriksen in the build-up, a decision Arteta was visibly unhappy about on the touchline.
"I haven't seen the action [again], but they said it was a soft foul," Arteta said. "It is just the consistency. There is nothing we can do now, it is too late.
"We're very disappointed that we haven't won the game. The game was there for the taking. We haven't won it because we lacked some discipline in some moments and we weren't ruthless enough in front of goal."