The Potters boss was speaking after he watched the Dutchman come off the bench to grab a brace to help the Gunners to a 3-1 victory to move them up to seventh in the table.
Pulis told reporters: “He changed the game. We looked comfortable until he came on, we didn’t look under any threat.
“Asmir didn’t have a shot to save until that point. He picked the ball out of the net once in the first half and wasn’t really troubled. He scored two goals and changed the game.”
Despite the defeat, which leaves Stoke in ninth position in the league, Pulis believes that for large periods in the game his side were the better team, but concedes they lacked the belief that they could go on and win.
He said: “We picked up and looked the better team. It’s just having that belief.
“We have to retain the ball better than we did. We have players who will score goals, but we’ve got to learn to retain the ball better than we did at times.”
Having played in Europe in midweek, Pulis refused to blame the club’s Europa League commitments for his side’s defeat.
This is the third time this season Stoke have followed a Europa League game with a Premier League defeat, but Pulis insists it is just a coincidence.
He continued: “The lads worked hard again today. If you look at the running stats and everything else, we’re not far off where we’ve been when we’ve been winning games.”
Pulis has turned Stoke into an established Premier League side since their promotion to the top flight in 2008, but he was quick to note that the club’s aim is simply to stay in the league.
“I don’t think our football club will win the Premier League for the next few years,” he added.
“Our biggest aim is to stay in the league. That’s our priority, what we want to do, is do well in cup competitions. That means the Europa League, the FA Cup, the Carling Cup.
“We had a great time last year going to Wembley, it was absolutely fantastic. It galvanised the city, it galvanised the club and we will do our best in all the cup competitions.