The London club arrived in Lisbon on the heels of their first back-to-back losses this season, a 2-0 defeat by Manchester City in the League Cup final and a 2-1 upset by Championship side Southampton in the FA Cup quarter-finals.
"We have to have some perspective on how difficult what we have done up until now has been," Arteta told reporters on Monday. "Feel the pain, use it to improve.
"We are very clear what happened and why it happened. This is football."
With Arsenal reduced from four competitions to two, Arteta said calm thinking rather than panic was key as his players look to respond on the European stage.
"I think what you have to be is clear, understand why it happened," he said. "And when you understand that, be better, and that is what we have to do."
Neither Bukayo Saka, Eberechi Eze nor Jurrien Timber will be available for the first leg after the trio did not travel to Portugal due to injuries, although Arteta said he was hopeful they could return at the weekend.
There was better news elsewhere, with Gabriel Magalhaes, Declan Rice and Leandro Trossard all available after being spotted in training.
Arsenal face a Sporting side unbeaten at home in Europe this season, with the Portuguese champions looking to seize the initiative in the two-legged tie.
Sporting midfielder Maxi Araujo shrugged off suggestions Arsenal are favourites on Tuesday.
"There are no favourites in this play-off," he told reporters. "They are playing well, we are too."
Sporting manager Rui Borges said the fact Arsenal have lost successive games means little.
"No, I don't believe in that and great teams always want to win," Borges told reporters. "They will be more focused, willing to show their collective individual capacity and so I think it will make it more difficult for us."
The second leg is on April 15th at the Emirates Stadium.
In between the two legs, Arsenal return to their Premier League title quest when the league leaders host Bournemouth on Saturday.