The Gunners lost their third game in a trot at Southampton on Saturday through a 1-0 scoreline and have scored just once in their last three games.
Arsenal have surrendered their advantage in the top four race by losing four of their last five league games and are now behind Tottenham and Arsenal, having played a game more.
Bothroyd conceded that problems are mounting up for Arsenal at a crucial stage of the season and the run of games they have coming up has made the situation bleak for the club.
He stressed that lacking a goalscorer is coming back to bite Arsenal given their top-four rivals Manchester United and Tottenham have played such as Cristiano Ronaldo and Harry Kane in their squads.
The former Premier League star said on Sky Sports: “When you look at Arsenal, no goals in three games [one goal] and three losses.
“And then you have got Chelsea away, Man United at home, West Ham away and then you have got the north London derby away.
“Things are looking bleak at the moment.
“You look at Man United, they have got Ronaldo to score goals, you look at Tottenham, they have got Son and Kane, but Arsenal don’t have a goal threat like that.
“That’s why it worries me and it must worry the manager.”
Arsenal will hope to turn their season around in a London derby at Chelsea on Wednesday night.