Counterpart Roberto Martinez also faced questions about his future, with Everton ending the season without a trophy and the team 11th in the English Premier League.
"I share the drive the club has, which is getting into the Champions League and situations where we can win silverware," Martinez said. "Every season, we are developing and reaching certain signs where I feel we can please our fans and bring the silverware they deserve.
"But clearly, at moments like this of true disappointment, it is very difficult to see through that the real good things we have developed over the last three seasons."
Martial set up Marouane Fellaini's opener in the 34th minute against his former club. David de Gea saved Romelu Lukaku's penalty early in the second half to preserve United's lead after Ross Barkley was brought down by Timothy Fosu-Mensah but Gerard Deulofeu's cross was inadvertently turned into his own net by United defender Chris Smalling with 15 minutes remaining.
Martial's winner was a slick completion of a rapid counter-attack that prevented extra time. The 20-year-old French forward linked up with Marcus Rashford on the left flank and then played another one-two with Ander Herrera before slotting the winner.
The 11-time FA Cup winners will face either Crystal Palace or Watford in the final, with the second semifinal played early today.
It seems the FA Cup would be only a consolation prize for United if it does not follow a top-four finish in the Premier League to secure a route back into the Champions League.
"It's not for me to judge, it's for the board of Manchester United," van Gaal said following months of reports not disputed by the club that former Chelsea manager Jose Mourinho has been lined up as a replacement.
With four games remaining, United remain fifth, four points behind Arsenal, who played relegation-threatened Sunderland early today.
Crosstown rivals Manchester City are a further point ahead in third after beating Stoke City 4-0 in one of four Premier League games yesterday.
Newcastle remained in the relegation zone despite coming from 2-0 down to draw 2-2 at Liverpool, who announced before the game that defender Mamadou Sakho failed a drugs test before a Europa League game last month.
Southampton kept alive their outside shot at qualifying for the Europa League by compounding already-relegated Aston Villa's woes. Dusan Tadic scored twice in a 4-2 win for seventh-place Southampton, while deposed champions Chelsea are a place behind after cruising to a 4-1 victory at Bournemouth, who have already secured a second season in the Premier League.
Meanwhile, the race to secure automatic promotion to the Premier League could not be closer after Brighton's 3-1 victory at relegated Charlton and Middlesbrough's 0-0 draw with Ipswich ensured both teams joined Burnley on 87 points with two games left.
Only two of the three will definitely go up without resorting to the lottery of the playoffs, yet no points and just three goals separate them, with Middlesbrough due to host Brighton on the final day of the season.
Middlesbrough remained second on goal difference after failing to break Ipswich's resistance at the Riverside Stadium.
The result ended the faint playoff hopes of Ipswich, for whom All Whites centre back Tommy Smith played the full 90.
Hull and Derby County are already guaranteed playoff spots. All Whites striker Chris Wood opened the scoring in Leeds United's 2-2 draw at Hull, following his brace against Reading the previous weekend, taking his goal tally for the season to 12.
Sheffield Wednesday, helped by yesterday's 1-1 draw at Derby, are likely to secure the final berth.
Cardiff City, 2-1 winners over bottom-placed Bolton Wanderers, retain a theoretical chance of pipping Wednesday and travel to Hillsborough this weekend.
The relegation of MK Dons to League One was confirmed after just one season following their 4-1 defeat by Brentford.
- Agencies
