Ajax ended the night level on eight points with Olympique Lyon, 7-1 winners at Dinamo Zagreb, but were overtaken by the French side on goal difference.
Real opened the scoring after 14 minutes when a pass from Kaka beat the Amsterdam offside trap and put Jose Callejon in a scoring position.
Ajax, who needed only a draw and started with a seven goal advantage over Lyon, were unlucky when first half goals by Nicolas Lodeiro and Vurnon Anita were ruled offside.
Four minutes before the interval Real's Karim Benzema set up Gonzalo Higuain to double the lead and in the second half only Sulejmani came close to bringing his side back in the match when his curved shot hit the bar. Callejon made it 3-0 for Real in stoppage time.
"We were so close and if you go out like this it tastes bitter," Ajax coach Frank de Boer told NOS-TV.
"I noticed some tension in my team in the opening phase but after the opening goal we did well and scored two good goals which were wrongly disallowed.
"It should have been 2-2 at half-time as we were not worse than Real who didn't really play with everything they've got."
