United have gone five games unbeaten in the Premier League.
Rashford scored in United's 2-1 win over champions Manchester City at the weekend to take his tally to 10 league goals for the season, already equalling his best return in the top flight midway through the campaign.
The former Chelsea midfielder has been tipped to leave United in January, having found his place in Solskjaer's first-team plans come under threat during the opening weeks of the season, with Serie A clubs including Milan and Inter said to be interested. "It doesn't happen that you feel great every time you walk onto the pitch".
Lingard is yet to score in the Premier League this season and he has only started six of Manchester United's 16 games in the top flight this term.
"The young boys will improve that as well in the next few years and hopefully the rest of the year".
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"Because we've come through a sticky patch with bad injuries and bad results, and we're looking brighter now".
"Inside [the club], we've always had belief in what we're doing. I see these boys every day in training, the attitude and skills they have got, so I'm not that anxious".
Fred was hit by a missile as he went to take a second-half corner in the 2-1 Premier League victory at the Etihad Stadium, where a fan appeared to aim a monkey gesture at the Brazil worldwide and team-mate Lingard.
A 41-year-old man was arrested on Sunday in connection with the allegations, before being bailed pending further investigation.
Solskjaer backed Rashford to emulate five-time Ballon d'Or victor Ronaldo, who has bagged three Premier League titles and the Champions League with United before leaving for Santiago Bernabeu in 2009.