Sanchez wasn't among the United squad heading across the Atlantic because there was an issue with his visa after the forward accepted a 16-month suspended sentence in Spain over a tax issue.
Coming off a superb win against the league leaders in the previous weekend, Mourinho's Reds faltered against a determined West Brom, who had nothing to lose.
Not even a 2-0 victory over Brighton was enough to mellow United manager Jose Mourinho, whose joy at beating Liverpool last weekend in the league was wiped out by a Champions League exit to Sevilla.
Former United skipper Vidic feels that Sanchez's quality and experience can be the difference in United's chance in chase fo trophies.
The winger refused to sign a new deal with Arsenal and was highly speculated to reunite with his former boss Pep Guardiola in Manchester City.
The winger has made a bright start as he scored on his debut and Sanchez has set a new record on social media as the deal announcement post was 'the biggest United post on Instagram'.
The Chile forward created goals for striker Marcus Rashford and midfielder Ander Herrera before coming off with around 20 minutes remaining.
Sanchez, who joined United over neighbor and Premier League leader Manchester City, said he was "thrilled to be joining the biggest club in the world."
A direct swap deal with no fee included, the former Borussia Dortmund player who spent two seasons under Mourinho will now sport the Gunner's crest, taking Sanchez's position.
A week before it was both City and United who were in the race for Sanchez, but the league leaders backed out after the management felt that the wages demanded were too lofty.
Manchester City didn't want to make Sanchez the highest-earning player at the club.
Arsenal have set their eyes on three targets this winter which include Argentine Cristian Pavon from Boca Junior, Malcolm from Bordeaux and Aubameyang from Borussia Dortmund.
Despite Manchester City being favourites to sign the Chilean from Arsenal, Jose Mourinho has entered the race as he looks to sign both Sanchez and Ozil from the North London club.
Ozil has been at Arsenal since September 2013, when he moved from Real Madrid, while Alexis joined the Gunners in July 2014 from Barcelona.
Wenger feels the Chilean works hard at the training and he will soon be able to get back to scoring goals.
After suffering back to back defeats in the World Cup qualifiers to Bolivia and Paraguay and a thumping defeat to Liverpool in the EPL, Sanchez bashes the Pundits for their criticism.
Sanchez was linked to Manchester City but Arsenal ensured that the move fell through at the last minute.
Mesut Ozil delivers a heartfelt apology to the Arsenal fans on social media after the Gunners were humiliated by Liverpool at Anfield 4-0.
Sanchez is expected to be back in Arsenal's lineup for the team's most high-profile match in the league so far.
As the speculations fuels up, the Brazilain and Barcelona winger Neymar Jr is set to break all records to join the Les Parisians. The Ligue 1 runners-up are nearly roping in troubled Arsenal forward Alexis Sanchez as well.
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