Arsenal have kept four clean sheets, the second highest in the league, and are among the teams who have conceded the least goals so far this season.
"We (United) gave them two or three chances, but we have a great goalkeeper as well and he did well also, so defensively I think we can build on that," Mertesacker was quoted as saying on the club's website.
"Now we have a little break and in two weeks we come together again and we have to remind ourselves what we can do," the 31-year-old German said ahead of the international break.
Left back Nacho Monreal was full of praise for team mate Sanchez, who has scored six goals in his last three games.
"He (Sanchez) scored 25 goals in all competitions and this season he has started really well," Monreal said.
"We need Alexis to score more goals and we are happy for him because he's a really important player for us."
Former Barcelona winger Sanchez was forced off in the 81st minute after picking up a knock and manager Arsene Wenger confirmed it was not serious and that Sanchez will travel to play for Chile during the international break.
"He (Sanchez) has a little groin problem. Unfortunately he goes to Chile. You cannot stop him from going to Chile and he loves so much to play for his country," Wenger said.
"Hopefully he will come back in good shape."
The 65-year-old Frenchman also heaped praise on forward Theo Walcott, who set up two of the three goals on Sunday.
"He (Walcott) did really fight today and showed he can fight, commit and protect the ball as well. He is gaining some aspects of his game as a centre forward and they are improving," Wenger said.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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