"The gap would have been too big if we had drawn or lost. It would have been very difficult," Van Gaal told British media
"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."
United welcome 12th-placed Everton after the international break, followed by a trip to second-placed Tottenham Hotspur. They also host current leaders Leicester City on May 1.
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Michael Carrick believes that the derby win was worth more than three points, considering league situation prior to the two-week break.
"The position we are in the league meant it was a must-win," the midfielder told British media.
"We had to get the three points before the international break to give us a boost and something to go at when we come back."
United's only route to Champions League next season is by securing a top-four finish in the Premier league after they were ousted from the Europa League by Liverpool last week.
(Story refiled to fix typo in headline)
(Reporting by Arnab Paul in Bengaluru; Editing by John O'Brien)
