Ozil, who moved to the Emirates Stadium from Real Madrid in September, started brightly for Arsene Wenger's side but has struggled of late and has been criticised by a section of the club's fans.
Parlour acknowledges that any foreign import requires a settling-in period and does believe the Germany international will eventually prove his worth. However, he wants to see better performances as the Gunners make their way through a tricky fixture list.
"Ozil started really well and you can see the quality he’s got, but he needs to improve quickly because they need results," Parlour told Goal. "If they don’t get results you can quickly slip away. They’ve still got every chance, they’ve got to go to Chelsea, they’ve got Manchester City at home, and it’s still feasible to go on and win the league.
"He’s taking time to settle in. [Robert] Pires had a first poor season and after that he was fantastic. He’s just getting to grips with it. The Premier League is a lot quicker. In Spain they build up the play a lot slower. They dictate the pace of the game a lot at Real Madrid and in the last third they’re lightening when they change pace.
"It’s a different way of playing football. This league is a lot harder, a lot more competitive. If you’re playing somebody at the bottom, Crystal Palace for example, you’ve got to be right at it. If you go to Selhurst Park you know you’re going to be in a game. When you’re at Real Madrid or Barcelona and you’re playing the bottom teams it’s normally four or five nil, a stroll in the park. Here it’s a lot more competitive. He’s getting to terms with that."
Parlour also says it takes time to adjust to the way the game is called in England.
"I’m sure the referees are different, as well," he said. "In Spain you get a lot more free kicks for little tugs, and I’ve seen him go down a few times and is looking round saying, ‘Where’s my free kick?’ but in England you don’t get them. So he’s got to get used to the whole scenario of the quick pace, the competitive games, the tough games, and I’m sure he will come to terms with it."
Parlour, who won four FA Cups during 12 years with Arsenal, believes the competition may be Wenger's best chance of silverware this season.
The Gunners welcome Liverpool for the fifth-round clash just eight days after the Reds' dominant Premier League win at Anfield, and Parlour says it is the perfect opportunity to aim for revenge despite the looming Champions League clash with Bayern Munich on Wednesday.
"They’ve got to look at the FA Cup, that might be the trophy they can win," he added. "I know it’s a difficult game after seeing Liverpool last week – 4-0 up after 20 minutes didn’t help. It’s going to be a tough game. Wenger will have one eye on Bayern Munich, we don’t know what sort of team he will put out, I think it’s a game he really has to get a result in because after losing 5-1 against Liverpool in the league the week before, you need to get revenge.
"I’m sure he will put a very good side out, and I think it’s there for the taking this year. Manchester City play Chelsea, so one of the top sides will be out, and you’ve got a couple of Premier League clashes as well. You only need a bit of luck in the draw; another home tie, maybe against a Championship side, and you’ve got half a chance of getting to Wembley."
Ray Parlour was talking to Goal as part of the Budweiser Open Trials, in association with BT Sport, where he will be assistant coach to Steve Clarke and help choose and manage the amateur footballers who will play in front of professional scouts at Wembley in April.
Watch the first part of the Budweiser Open Trials on BT Sport on Saturday, March 8, as part of its FA Cup coverage, and subscribe to YouTube.com/BudweiserUK to keep up to date with all the action.