Everton’s strong start to the season was dampened by the 3-0 loss against Aston Villa on Saturday evening and the Toffees also have concerns with injuries.
Rafael Benitez’s side do not have much rest as they face Championship team Queens Park Rangers early next week in the third round of the EFL Cup.
Goodlass admitted to being worried by all the injuries the Toffees have picked up so far going into the game next week.
The former Toffees winger added though that he thinks Benitez should definitely pick a strong squad to face the Hoops as Everton have more than a fair chance to go all the way and win the EFL Cup.
Speaking on BBC Radio Merseyside post match, Goodlass said: “I’m a bit worried over Tuesday.
“How long will Richarlison [be], Calvert-Lewin it looks like will be a bit, is Pickford going to be out?
“We play QPR on Tuesday and we want to put a team out that’s going to win it because we’ve got a great chance of getting some silverware.
“I just think we’ve got to put a team out, but I just think longer term how long will the lads be out.
“Tuesday we’ve got to think about picking a team to win that.”
Everton’s last picked up a domestic cup when they won the FA Cup in the 1994/95 season and they have never won the EFL Cup.