Erik ten Hag's side extended their winless run to five matches with a 0-0 draw against in-form Villa at Villa Park.
Despite lacking attacking threat, it was a resolute defensive performance from United, who had conceded six goals in their previous two matches against Tottenham and Porto.
Jonny Evans was named Man of the Match and Berbatov insists the Red Devils should be 'ashamed' of that given his age.
He also believes the criticism on boss Ten Hag 'will only grow', with the side currently 14th in the table after Sunday's draw.
Dimitar Berbatov has slammed Manchester United following their stalemate with Aston Villa
'Everybody on the pitch should be ashamed because Evans is man of the match at 36', the Bulgarian said speaking on Sky Sports.
'The criticism will continue to grow, because United need to win to get the points. They are 14th in the table which is unbelievable.
'The only thing to correct it is to get the points buy with the way they're playing at the moment that's going to be hard to do.'
The draw against Villa ensured United have made their worst start to a league season in 35 years with just eight points from seven matches.
This slow start to the 2024-25 campaign comes after United recorded their lowest finish in Premier League history last season, whenTen Hag's side ended up in eighth place.
The last time that United picked up eight points or fewer from their first seven league fixtures was in the 1989-90 season.
United had just seven points after seven games in September 1989 and they went on to finish 13th in the old First Division in what was Sir Alex Ferguson's fourth season at Old Trafford.
Speaking to BBC Match of the Day after the game, he said: 'I think the performance of United was very good. Defending and in possession we controlled the game. It was in the balance. We created chances but not loads.
'Also Villa didn't create too many chances. It was balanced. We hit the crossbar, they had a shot blocked.
'We had that resilience, the whole season. We conceded three against Tottenham [in a 3-0 defeat last weekend] because we were down to 10 and we still went for the win. But for the rest this is our fourth clean sheet. This tells you we are in a good direction.
'Now also we improve defending counter attacks, and we improve controlling possession. But also we have to improve in the final third.'