Fulham assistant manager Christian Damiano said his side deserved a share of the points.
"We had the ability to react with quality and in the end it was a beautiful draw," said Damiano.
"We deserved a draw. We had many corners and set-pieces and for us it is fantastic. The point will give us more confidence and hope for the future."
However Steve McClaren was left in shock after Middlesbrough threw away a two-goal lead in the last minute at the Riverside.
They had seemingly been cruising to three points after Massimo Maccarone's double, yet Sean Davis and Facundo Sava grabbed last-minute goals to earn an surprise draw.
McClaren was stunned, saying: "There's a bit of shock and devastation at the moment. But that's football. Sometimes it teaches you harsh lessons and we got one today.
"But I got a fantastic reaction from the players. They were angry and not very pleased with each other and that's what I wanted to see. I want to make sure that feeling doesn't go away so they will know what to do next time."