Pogba, 27, conceded a penalty to allow the Gunners to grab a 1-0 victory.
“Paul knows in that exact instance he could’ve done better and held his hand up,” said Solskjaer.
Frenchman Pogba has played nine times for United this season having suffered an injury-hit campaign last term.
An ankle problem restricted the former Juventus midfielder to 22 appearances in 2019-20, while he also tested positive for coronavirus in August.
Solskjaer may rest Pogba and decide to go with Dutch midfielder Donny van de Beek in Wednesday’s Champions League group game at Istanbul Basaksehir (17:55 GMT).
“Every player is frustrated himself and is disappointed after defeat,” said Solskjaer. “We need consistency from every one of our players.
“Paul has gone through a difficult period with an injury last season and Covid, now working up to full fitness. We have seen plenty of positives now and hopefully more can continue.
“It’s high intensity and the fitter you are the better.”
Manchester United will be without midfielder Jesse Lingard who has not travelled while full-back Alex Telles is unavailable after recently testing positive for coronavirus. Centre-back Eric Bailly remains sidelined.
Basaksehir could field former Manchester United right-back Rafael, after the Brazilian started in Sunday’s win at Konyaspor.
Ex-Liverpool defender Martin Skrtel should start at the back, alongside on-loan Celtic full-back Boli Bolingoli.
Chances of qualifying?
Data analysts Gracenote say Manchester United have a 91% chance of progressing to the knockout stages of the Champions League.
Simon Gleave, head of sports analysis at Nielsen’s Gracenote, said: “Manchester United began the Champions League as third favourites to progress from Group H. Two matches later and United are firm favourites having beaten both of their main rivals for a place in the knockout phase.
The Euro Club Index estimates that the Red Devils have a 91% chance of finishing in the top two and a 60% chance of winning Group H. Two matches against bottom club Istanbul Basaksehir now should seal United’s place in the last 16.
- This will be the first meeting between Istanbul Basaksehir and Manchester United in any European competition.
- Istanbul Basaksehir’s only previous experience against English opponents was in the qualifying phase of the 2018-19 Europa League, losing 1-0 on aggregate to Sean Dyche’s Burnley.
- Manchester United have lost their past two away games against Turkish opponents in European competition – 1-0 v Galatasaray in November 2012 and 2-1 v Fenerbahce in November 2016.
- Manchester United are looking to win their first three matches in a Champions League group stage for a ninth time – no team has ever failed to qualify after winning their first three games in a group stage.
- Istanbul Basaksehir are one of three teams yet to score in the Champions League, along with FC Midtjylland and Marseille. However, the Turkish side have had more shots than either of those two sides (23) and only five fewer than Manchester United (28), who have scored seven times.
- Against RB Leipzig, Man Utd striker Marcus Rashford became only the fifth player in Champions League history to score a hat-trick as a substitute. All nine of Rashford’s goals in the competition have come in the second half, the most of any player without scoring in the first half or extra time.
- Manchester United forward Mason Greenwood has six goals in major Uefa European competitions as a teenager (five Europa League, one Champions League), the joint-most of any English teenager along with team-mate Rashford. He is also looking to become the third Englishman to score in his first two starts in the Champions League, after Rashford in 2017 and Daniel Sturridge in 2010.