Spurs were beaten 1-0 at White Hart Lane on Sunday as Tomas Rosicky opened the scoring early on and the Gunners picked up a hard-earned three points.
|4/1||Tottenham are 4/1 to beat Benfica in the Europa League|
"The building process has to start in pre-season," Sherwood told BBC Sport. "Liverpool took a step back to move forwards. It requires patience.
"Whether Spurs want to do that I don't know. Whether they want me to be the person to do it remains to be seen."
The former Spurs midfielder has acknowledged he is "always on trial" and wants to stay in the White Hart Lane hot seat, despite a difficult run of results.
He added: "I've learned more in this last week as a manager than I did when we were going through the easy period when we were winning games.
"I think I've got the character for it and I want everyone to come along with me. I'm not crying about it - I knew what I was getting involved in. I'm playing the hand I was dealt.
"I'm always on trial, from all angles. I knew that would be the challenge but it's one that I relish."