Traffic notices in north London have revealed that Arsenal are expecting to show off the trophy in an open-top bus tour around Islington the day after Saturday's final.
But Meyler relishes Hull's role as underdogs and believes Arsenal must cope with the burden of expectation as they attempt to end a lengthy wait for silverware.
"Nobody expects us to win it and obviously they haven't won a trophy in nine years and they've got their posters up in London about their parade next week and credit to them," he said.
"I'd rather be the underdog. People are delighted when the underdog wins - I don't think many people want Arsenal to win.
"The pressure is all on them to win it. We have not been given a chance in the last two years - we were not favourites to go up last year and we were favourites to go down this year.
"But being the underdog isn't the worst thing in the world and we've just got to use it to our advantage. Nobody expected Wigan to win it last year but they made it difficult for Manchester City the whole game and they deserved to win it.
"It gives great hope for all of us, and you can also look at Sunderland and the teams they beat in the League Cup. It just shows it is 11 against 11 and if you want it more than the fellows you are up against then you can win."