The Frenchman's position at the club has been called into question in some quarters following defeats to Manchester United and Blackburn Rovers, with the Gunners already 11 points behind the Red Devils in the Barclays Premier League table after just five games.
However, Wenger insisted he wasn't fazed by the speculation surrounding his position, and is hoping to remain in charge in north London for another 14 years.
"I am not bothered at all by this speculation," said the manager defiantly.
"I have had 14 years at this club and kept them 14 years in the Champions League. I hope it lasts another 14. I can understand that people are unhappy and criticise, but you know as well as I know that people are very quick to go overboard."
"When we do well we take all the plaudits, so we have to take all the blame when it doesn't go as well - but we have, on both sides, to take some distance. When it goes well we must not completely believe what people say - and when it does not go as well, we must not completely believe it."
The Gunners went behind in their third round tie against the Shrews, before goals from Kieran Gibbs, Alex Oxlade-Chamberlain and Yossi Benayoun rescued the tie for the hosts.
It was the full-debut performance of Oxlade-Chamberlain which particularly pleased the boss, who brought the England youth international to the club this summer from Southampton.
"You could see that he will be a first-team player here, that is for sure. He has still things to work on but, very quickly, he will be knocking on the door."