A week that started with manager Ole Gunnar Solskjaer under pressure after a below-par performance in a home draw against promoted Aston Villa ended with a second memorable victory in a matter of days.
Fresh from deservedly seeing off Jose Mourinho's Tottenham 2-1 on Wednesday, United won by the same scoreline at the Etihad Stadium on Saturday thanks to a breathtaking start and impressive gameplan.
Solskjaer's side could have added to goals from Marcus Rashford and Anthony Martial in a fine first half that laid the foundation for the 2-1 victory, which moved them to within five points of fourth-placed Chelsea.
"I think you need to look after your own results, don't look elsewhere, keep winning games," said Maguire, the world's most expensive defender.
"We've won back-to-back games against Spurs and City. We've got another big game next week now (at home to Everton).
"The top four is in sight but we just keep looking after our own results, keep trying to get the three points and keep improving."
United struggled to score goals in the early months of the season but Rashford, Martial and the fleet-footed Daniel James showed they can scare any side on Saturday.
"Over the last month or so, I feel like as a defender I look at the forwards and think they're going to score goals," Maguire told MUTV.
"At the start of the season we didn't really score more than one goal in a game but now I think it's a few games on the spin where we're back to scoring goals.
"They're a big threat, they're top players, great talent and I think it's all coming together now."
United are unbeaten in five Premier League matches and have secured their first back-to-back league wins since March.
There is a growing confidence within Solskjaer's squad and Maguire is targeting more improvements after captaining the side to victory in the blue half of Manchester.
"We feel like this year we haven't got results in some games where we feel we deserved the three points," he said.
"I think the last two games, I don't think anyone can question that we've deserved both victories."