The Gunners pulled off the result, despite being without Pierre-Emerick Aubameyang, Kieran Tierney and Bukayo Saka.
Alexandre Lacazette came closest to breaking the deadlock, hitting the crossbar with a second half free-kick.
The point moved the Gunners up into eighth position, just six points off a Champions League qualifying position.
But Carragher feels Arsenal can only secure Europa League football should be the summit of their ambitions this season.
Asked what Arteta’s target should be, Carragher said: “To be playing European football next season. They are still in the Europa League so that’s an avenue for them for Champions League, there’s no way they’re going to get top four.
“But can they sneak into the Europa League if it goes down to seventh position? I think for Arsenal where they were at the start of this season they wouldn’t be any hope of the title
“But I think they would’ve wanted to challenge for top four after winning a lot of big games, winning the FA Cup, I think that would’ve been the expectancy to challenge.
“There’s still a long way to go, they’ll be having an eye on next season as well. If they’re in the Europa League next season they’ll have done OK, considering where they were.”
Arsenal cannot finish in top four after 0-0 draw with Man Utd – Carragher
You may be interested
Pastor sentenced to life in jail for raping, impregnating his 14-yr-old in-lawWebby - January 21, 2022
A 38-year-old businessman and Pastor, Ofure Rey Siakpere, was on Wednesday, January 19, sentenced to life imprisonment by an Ikeja…
Trigger-happy officer assaults lady, shoots at civiliansWebby - January 21, 2022
Spread the loveTrigger-happy officer assaults lady, shoots at civilians. A trigger-happy police officer who was formerlya SARS operative was seen…
BREAKING: I killed my 5-yr-old student with N100 rat poison — Proprietor confessesWebby - January 21, 2022
Abdulmalik Tanko, the proprietor of Noble Kids Nursery and Primary School, Kawana, Kano, has narrated how he used a N100…