Louis van Gaal says Manchester United's top-four hopes would have been over had they lost to Manchester City, but believes they now have a "big chance" of Champions League qualification.
Marcus Rashford's goal earned a 1-0 derby win over City on Sunday.
Van Gaal's side are sixth in the Premier League, but lie just a point behind their local rivals in fourth.
"The gap would have been too big if we had drawn or lost. It would have been very difficult," said the United boss.
"Now it is in our own hands but we have to win our games. We have more home matches than away and we don't lose so much at Old Trafford - so we have a big chance."
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United won at Etihad Stadium for the first time since December 2012, just three days after being knocked out of the Europa League by Liverpool.
"I thought we played fantastic in the first half and the second half was a test of survival because we were very tired," added Van Gaal.
"We had only two days to recover after the Liverpool game and that is almost not possible.
"We have seen the result from Southampton today. Liverpool were 2-0 up at half-time and at full-time it was 3-2 to Southampton.
"I have not seen the match but I can only conclude it was because of tiredness and that is what we have done to them."