Foster watched videos of Spurs players taking penalties on an iPod and then saved from Jamie O'Hara as United lifted the cup after winning the penalty shootout 4-1 following their goalless draw at Wembley Stadium.
FIFA president Sepp Blatter has resisted the use of any form of video technology, especially to determine if the ball has crossed the goalline, for many years. But the idea of using an iPod as a tactical aid is new and not against the laws of the game.
Former Premier League referee Graham Poll told the Daily Mail on Monday that using iPod technology "had the potential to exploit a loophole in the laws which should be referred to FIFA."
An FA spokesman said: "What happened was not against the rules so we will not be investigating the matter further."
Spurs were last involved in a penalty shootout a year ago when they lost to PSV Eindhoven in the UEFA Cup.
In that game, O'Hara fired a shot to the left of the goalkeeper and on Sunday he sent Tottenham's first penalty the same way and Foster saved.
"Just before the shootout I was looking at an iPod with goalkeeping coach Eric Steele and it contained images of Tottenham's players taking penalties," Foster said.
"They told me for Jamie O'Hara I should stand up and be strong and he would probably go the way he did. I have done a lot of research before but this is an innovation we have brought in at the club."
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