The Emirates side went a goal down after just ten minutes thanks to a Christian Eriksen tap-in, then saw the deficit doubled 30 minutes later when the Swiss international brought down Heung-min Son in the box.
Harry Kane converted the penalty before Alexandre Lacazette fired home just before the half-time whistle, with Arsenal ultimately battling back to a 2-2 draw courtesy of Pierre-Emerick Aubameyang, but a more precise approach from Xhaka could have resulted in three points.
Regardless, Emery feels the midfielder had a good game other than the foul and has backed his man to improve as Arsenal look to cut out their mistakes and climb the Premier League standings.
“We were speaking this morning,” the manager said of Xhaka. “[Make a] mistake, recognise that mistake, learn, correct it, improve and repeat with success. We could speak about every player's mistakes in every training session and each match.
“Only, some mistakes can be 'big picture' because the consequence is more [apparent]. But really we can't have more mistakes like that after they score a goal against us or if we haven't scored.
“But I am focused on the good things, on the positives. Xhaka has a big character and he's very important for us.”
Asked if the 26-year-old brings something to the team that fellow central midfielders Matteo Guendouzi and Lucas Torreira do not, Emery continued: “Of course, he gives us very good balance in the middle with the ball and without the ball.
“He's very important for us. We can talk about the defects of any player, for him too, but we can speak about the very positive performances he gives us in most matches [too].”
Arsenal travel to Watford's Vicarage Road on Sunday with one eye on three points against a side who recently re-hired Quique Sanchez Flores to replace Javi Gracia, who was shown the exit door after failing to win any of the Hornets' first four matches.