Newcastle finished 11th in the Premier League last season despite spending the majority of the campaign locked in a relegation battle.
Following a £92million January splurge, The Magpies are expected to strengthen again during the summer transfer window having already secured the £15million signing of Matt Targett from Aston Villa.
The ambitions of the club under new Saudi-backed ownership are to break into the top half of the Premier League but Merson feels that a cup run should be the priority.
"Newcastle should be happy finishing tenth next season if they can put together a good cup run as well,” the former Arsenal forward said in his Daily Star column.
"They have got to start turning up in the cup competitions because too many managers have mugged those off when they've gone there.
"Newcastle haven't won a trophy in so long and their fans need something to get excited about.”
Newcastle were knocked out of the Carabao Cup and FA Cup at their earliest possible stage last season and have not won a major domestic trophy since 1955.
Merson even suggested that most Newcastle fans would happily finish 17th if it meant winning a domestic honour.
"[The fans] need to be patient because they're not going to get into Europe next season,” he added. “I was up in Newcastle the other day for a charity dinner and I talked to a lot of fans who think they will spend £150m and buy this player and that player.
"They've just got to buy right, spend steadily and patiently on the right sort of players and build it up slowly.
"If Newcastle finish 17th and won a trophy, you'd have to be happy with that as a Newcastle fan surely?
"But the one thing they all said to me when I was up there is they have got something now they haven't had in a long, long time, and that is hope. Good luck to them.”