The north London club suffered a narrow 1-0 defeat as substitute Anthony Martial's goal in the final quarter of the match was the difference between the two sides. The latest defeat leave Spurs with 20 points after 10 games, three points behind second place United.
Manchester City, who are unbeaten in the Premier League, are sitting pretty at the top of the table some nine points ahead of Tottenham. Shearer believes the English capital club's latest loss to the 20-time English champions will be difficult for them to reduce the gap at the league leaders.
"Yes, it is early, but you could argue that Spurs' defeat at Old Trafford has already put them out of the title race," Shearer told the Sun.
"Eight points behind this Manchester City side is something to make up. Put simply, City would have to lose at least three games and right now they don't look like losing one. I can't see Manchester United slipping up in the way they did at Huddersfield many more times either."
United's win over Tottenham came days after West Ham United were forced to come from behind and beat Spurs 3-2 in the Carabao Cup. Spurs were knocked out of the cup competition, meaning they lost one more opportunity of winning silverware.
Mauricio Pochettino has already stressed that he would prefer to win the Premier League and the Champions League over the Carabao Cup and the FA Cup. Shearer has criticised the Argentine manager for not focusing on the cup competitions and stressed that he needs trophies in order to make Tottenham successful.
"Mauricio Pochettino's decision to play an under-strength side in the Carabao Cup look an even greater misjudgment than it did at the time. I don't doubt he will probably do the same in the FA Cup as well," the ex-England international stressed.
"Yet he only has to look at recent history to realise what these competitions mean in the development of a team. We are always being told what a great young Spurs side this is, but they need to win something.
"City might now be looking at bigger things but they got the club's winning mentality initially from their 2011 FA Cup win. The League Cup was also the springboard in both of Jose Mourinho's terms at Chelsea.
"Twice at Stamford Bridge he went on to win the League in the same season after the League Cup had been won. Last season after lifting it again, this time with Manchester United, his side went on to win the Europa League as well."
"Success has a habit of breeding success and, despite all the plaudits for Pochettino, he is going to need some."