The Gunners led the league for much of last season but eventually fell away in the final months, and Arsene Wenger's side were heavily beaten by both Liverpool and Chelsea in February and March respectively.
However, Smith has claimed that the Gunners can become serious contenders for the title if they match the sides around them.
"In order for Arsenal to challenge, and to be proper challengers, I think they've got to better against those title challengers," Smith told Sky Sports News.
"Down the years, they have a good record against Spurs, but you know at home, it is a nice early derby for the Arsenal fans and those matches don't normally disappoint."
Wenger's side begin their pre-season preparations against Boreham Wood this weekend.