After a run of three wins on the trot in the league, the Gunners suffered a minor hiccup in the form of a 0-0 draw against Crystal Palace at the Emirates on Thursday night.
The point meant Arsenal remained in the bottom half of the table in eleventh and some way away from their ambition of breaking into the Champions League spots again.
After a horror start to the season, Arsenal have turned the corner in the last few weeks and performances and results have been more encouraging and positive.
Wright believes there is a lot to look forward to with the emergence of Bukayo Saka and Emile Smith Rowe this season.
However, he insisted that the Gunners are still very much a side in transition and will need more time to show more tangible progress and climb up the league table.
The Arsenal legend said on Premier League TV after the draw with Crystal Palace: “I think it is very encouraging to see [Thomas] Partey coming on, he is going to make a big difference.
“Hopefully Gabriel Martinelli will come on as well and the emergence of Emile Smith Rowe and Saka, who were both quiet tonight, I think there is a lot to look forward to.
“It is very easy to get carried away with it, but Arsenal need to be where they are, in respect of climbing the league.
“But it is going to take some time.”
Arsenal will be looking to get back to winning ways when they host Newcastle at the Emirates on Monday night.