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United had only two shots on target but Anthony Martial's close-range finish was enough to earn three points.
"We didn't play so well," Van Gaal said. "We didn't create many chances.
"Everton are a very good team, much stronger away than at home, and it was a very tight game.  We were the lucky team today."
Manchester United have been dogged all season by criticism of their style of play - with Sunday providing the 15th occasion this season in all competitions that a match at Old Trafford has been goalless at half-time.
"We want to give entertainment for the fans, but the fans were entertained today because of the tension," Van Gaal said.
However, despite having the second-lowest goal total of any team in the top half of the table, United are just one point behind fourth-placed Manchester City and remain firmly in the race for the Champions League qualification places.
United, who had won 1-0 at City in the previous league match on 20 March, visit Tottenham next Sunday.
"If we lose today, the victory against Manchester City is worthless," Van Gaal said. "Now we are still in the race. We have a very important game against Tottenham."
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Manchester United manager Louis van Gaal has described his team's 1-0 Premier League win over Everton as a "stolen victory".