The Toffees have been relegation battlers for the last two domestic seasons in the top flight and they also made an initial shaky start to the current campaign.
The Merseyside club only managed to avoid relegation on the final day of the previous term and finished 16th the season before.
Thelwell stressed that he and everyone involved with the club are trying to get Everton back to the club’s glory days.
And he insisted that simply surviving in the Premier League cannot be marked as success for the Goodison Park outfit.
“I am not saying that just because we survived, we got the job done”, Thelwell said on BBC Sounds about avoiding relegation on the last day of the previous campaign.
“Because that is not a marker of success for this football club in any way shape or form.
“But I just hope in due course we can get Everton back to where it belongs.”
Everton are now picking up steam under the management of Sean Dyche, winning three of their last four games, but an acid test awaits after the international break when rivals Liverpool welcome the Toffees to Anfield.
