Louis van Gaal is confident Manchester United can win their final three league games of the season, even though two of them are away.

United travel to Norwich on Saturday afternoon then West Ham on Tuesday before completing their season with Bournemouth at Old Trafford. There is no guarantee picking up nine points will achieve the top-four finish the club demands but Van Gaal knows nothing less is likely to suffice and there is always the chance Manchester City will suffer an adverse reaction to going out of the Champions League so disappointingly in Madrid on Wednesday.

“We cannot rely on that – some teams are capable of coming straight back after a disappointment and City may be able to do that against Arsenal [on Sunday],” Van Gaal said. “We have done it this season so City might be able to do the same. I don’t want that, of course but it is possible. All we can do is win our remaining games, and we must. We have enough quality and mental strength to do it, and our injury list is now not quite so severe. We are only missing two or three players.”

Van Gaal said it is for the board to decide whether finishing fourth would constitute a successful season. Were United to manage that and lift the FA Cup a week later it would certainly be a more upbeat finale than has been envisaged, though the more pressing question is what happens if Van Gaal falls short of Champions League qualification.

“That is for the board to consider,” Van Gaal said, not for the first time. “All we can do now is concentrate on winning our remaining games, the Cup final at Wembley and the three league games before it. The pressure is very high for everybody now but especially for Norwich, because they might be saying goodbye to the Premier League.”

• This article was amended on 7 May 2016. It originally stated that Manchester United had yet to string three consecutive victories together in the Premier League this season. They won three matches in a row in September.