The Saints are one of four top-flight teams who are yet to celebrate a victory in any of their opening eight matches this season, picking up just one point and losing seven games, including each of their last three.
Pressure is beginning to mount on head coach Russell Martin, who was denied his first Premier League win of the season by a brilliant second-half revival from Leicester City last weekend, with the Foxes coming from two goals down to win 3-2 at St Mary's, netting a dramatic 98th-minute winner to snatch maximum points.
Southampton have found the net in each of their last four Premier League games, but only Crystal Palace (five) have scored fewer goals so far this season than the Saints (six), who sit 19th in the table and are now gearing up for a daunting trip to the Etihad Stadium to face reigning champions Man City on Saturday.
Attackers Cameron Archer and Ben Brereton Diaz were both signed by Southampton in the summer and while the former has chipped in with two Premier League goals - including one last weekend - the latter is yet to find the net for the Saints.
Southampton could do with "killer" striker Delap
Martin's side were also credited with an interest in 21-year-old striker Delap over the summer, with reports claiming that Southampton had a bid accepted by Man City.
However, fellow newly-promoted side Ipswich Town won the race for Delap's signature, signing him for an initial £15m plus £5m in add-ons, and he has since scored four goals in eight Premier League games for the Tractor Boys.
While McInerney has backed Southampton to score against a leaky Man City defence that have kept just one clean sheet in eight league matches this term, he also feels that the Saints are not blessed with a striker of Delap's calibre who could turn their fortunes around.
Speaking to Sports Mole, McInerney said: "I wouldn't be surprised if they score. Southampton have been scoring, they've got the odd goal, six in total so far, so it's not like they've scored none.
"They've not been truly atrocious at chance creation, it's just they haven't got maybe what Ipswich have got in Liam Delap. They haven't got a killer up front.
"[Cameron] Archer is a good player, [Taylor] Harwood-Bellis is an ex-City lad, [Aaron] Ramsdale is a good keeper, [Kyle] Walker-Peters has Premier League experience.
"They've got some good players, it's just a big ask for them [against City] and I would be amazed if they come to the Etihad expecting to get anything from this game."
McInerney not expecting Man City to stroll past Southampton
McInerney is not expecting Man City to cruise to victory on Saturday, though, adding: "I do think City will win, but I just don't feel it's going to be a stroll.
"Even if City win 3-1 or 4-1, I expect it'll be a little bit closer because that formula (in City's midfield) is still a little bit loose... If [Kevin] De Bruyne is back and available and if [Phil] Foden starts to find his form, we should be more than okay."
"The fixtures are reasonably favourable for City right now," McInerney continued. "This is the kind of game where [they need to] keep applying that pressure and win and hope that Arsenal and Liverpool drop some points. If both of them do, all of a sudden - despite City [potentially] not playing well - we'll be top of the table and still unbeaten."
Man City will be confident of success on Saturday as they have come out on top in 10 of their last 13 Premier League meetings with Southampton, who have not won at the Etihad since a 3-1 victory in April 2004.
Pep Guardiola's men - who cruised to a 5-0 win over Sparta Prague in the Champions League on Wednesday - currently sit second in the Premier League table and just one point behind leaders Liverpool, who travel to the Emirates Stadium to face third-placed Arsenal on Sunday.