The Japanese right-back, who has been bedevilled by injuries during his time in North London, lasted just nine minutes at the Emirates before being taken off after an awkward slip.
Tomiyasu was able to walk off the field, but he was seen leaving the stadium on crutches after the game, sparking fears about another lengthy layoff for the former Bologna man.
William Saliba was also a first-half casualty in the second leg with an apparent back problem, meaning that Arteta could potentially be without one of his defensive stalwarts for the business end of the Premier League season.
Speaking to the media after Thursday's penalty-shootout defeat, Arteta was unsure of the severity of Saliba's problem, but he admitted that Tomiyasu has seemingly picked up a severe issue which could render him unavailable for a while.
"Tomiyasu looks pretty serious, for his reaction straight away and what he said to me. Obviously, it's very early and difficult to know," arsenal.com quotes Arteta as saying. "William, I don't know. He had some discomfort and could not carry on, so we had to take him off.
In between Tomiyasu and Saliba's withdrawals, Arsenal broke the deadlock against the run of play through Granit Xhaka, but an astonishing 46-yard effort from Pedro Goncalves brought the visitors deservedly level early in the second half.
Arteta's men soon gained control of the tie in extra time, but Antonio Adan was an inspired man in between the sticks for Sporting, who withstood several Gunners attackers to force a penalty shootout courtesy of a 3-3 draw on aggregate.
Each side scored their first three spot kicks, but Adan kept out Gabriel Martinelli's effort before Nuno Santos sent Sporting through in front of the away end, thereby extinguishing Arsenal's hopes of continental glory for another year.
The North London club now only have the Premier League title left to fight for in the final weeks of the season, but Arteta does not view their Europa League elimination as a blessing in disguise.
"I cannot see it that way today. I don't know, if you go through the competition and win it, it's magnificent, if it's not, then it affects your plans in the league, that's a different story," Arteta added.
"We wanted to go through and we put everything into it, the effort the boys put when it wasn't our best day, individually and collectively, the hunger and the desire they showed to win, the way they were tracking back was incredible, they really wanted it and today it didn't happen.
"Looking at ourselves the game started difficult for us. Obviously, we lost Tomi very early in the game and we lost Saliba. That really left us with a difficult in-game management.
"We only had a window to make the subs, and a few players could not play 90 minutes. But still, we didn't find our rhythm and our flow. We allowed too many spaces, were late and didn't win enough duels there. We gave the ball away many, many times. Sometimes time after time."
Arsenal return to domestic duties with the visit of Crystal Palace to the Emirates Stadium on Sunday, where victory would take them eight points clear of Manchester City - who face Burnley in the FA Cup - at the top of the rankings.