Arsenal travelled to Lisbon after suffering back-to-back defeats for the first time this season, losing 2-0 to Manchester City in the League Cup final before a 2-1 FA Cup quarter-final exit to Southampton.
Arteta remained calm in his assessment but made it clear the squad must respond.
"We have to have some perspective on how difficult what we have done up until now has been," he said. "Feel the pain, use it to improve. We are very clear what happened and why it happened. This is football."
With Arsenal now competing in just two competitions, Arteta stressed the importance of clarity over panic.
"What you have to be is clear, understand why it happened," he explained. "And when you understand that, be better. That is what we have to do."
Arsenal will be without Bukayo Saka, Eberechi Eze and Jurrien Timber for the trip to Portugal due to injury, although Arteta suggested they could return at the weekend. There was a boost, however, with Gabriel Magalhaes, Declan Rice and Leandro Trossard all available after training.
Sporting, unbeaten at home in Europe this season, are confident of their chances. Midfielder Maxi Araujo dismissed the idea of favourites.
"There are no favourites in this play-off," he said. "They are playing well, we are too."
Head coach Rui Borges also warned that Arsenal's recent defeats could make them even more dangerous.
"Great teams always want to win," Borges said. "They will be more focused, willing to show their quality, and that will make it more difficult for us."
The second leg will take place at the Emirates Stadium on April 15, with Arsenal returning to Premier League action against Bournemouth between the two fixtures as their title challenge continues.
