The Gunners recorded a 3-0 win at St Andrews on Saturday evening to leave Blues in 19th place in the Premier League table going into the new year.
"As far as I know relegation is not decided until May and there are a lot of points at stake," the Blues boss told Sky Sports after the game.
"We have a lot of games to go still and we will start to panic if we are in this position in May.
"We will try to enhance the squad in January but we won't break the club in the transfer window.
"We have lost too many daft goals and we are not scoring enough.
"We have not found the potent formula in forward areas."