Two stoppage-time goals secured a dramatic comeback in the Toffees' Premier League encounter on Saturday.
Steven Pienaar's early goal put Everton ahead but Darren Fletcher, Nemanja Vidic and Dimitar Berbatov gave United a good lead before the Toffees' stunning late comeback through Cahill and Mikel Arteta.
Cahill told Sky Sports 2: "To be honest it's quite unreal but I think if we look at the chances we gave away and the chances we missed it's probably a fair result in the end.
"It was a tough game, really difficult. It just shows the fight. We've tried and tried the last couple of games and it hasn't happened. Today it was a great result."
Everton boss David Moyes was left fuming at the end when referee Martin Atkinson blew the full-time whistle just as his team were on the counter-attack.
"There's always ifs and buts," said Cahill.
"It would have been nice for a bit of commonsense at the end, to see whether (Edwin) Van der Sar would have saved it or whether we would have scored, but it happens."
Goalkeeper Tim Howard pulled off a string of stunning saves against his former club and was delighted with the fighting spirit showed by his team.
"The first half we dominated and we should have went in 1-0. Obviously they got the goal and in the second half they were powerful and went over the top of us.
"But we had spirit and we had fight and we got the point which was important."
Moyes felt the referee was wrong to blow the full-time whistle before Phil Jagielka got his shot away after Everton broke away quickly from a United corner.
"I think the two goals were scored after 90 minutes and they'd put up three minutes of extra time," the Scot told Sky Sports 2.
"I think you've said it's about three and a half minutes.
"We broke that fast, I don't think it could have been more than 8, 9, 10 seconds until we played the final pass and he blew up so that was wrong.
"It doesn't take anything off the way the players showed desire and character to get back into the game."
Moyes was particularly impressed with the display of American keeper Howard.
"The goalkeeper was fantastic today," he said. "I thought the goalkeeper was probably the difference.
"We could have lost but for the goalkeeper. In the same breath I thought the way the players played was excellent."
United manager Sir Alex Ferguson, who left Wayne Rooney out of his matchday squad following allegations about the England striker's private life, was left to rue two dropped points but took consolation from the performance of Bulgarian forward Berbatov.
"Football can do that to you," he said. "In a game of a completely comfortable position, we've thrown it away - simple as that.
"The last two away games have been like that. We lost a goal against Fulham with two minutes to go, and the same again today. We had chances to bury Everton and we didn't do it.
"We played some good football at times.
"Berbatov I thought was our best player. I thought he was absolutely brilliant today but that's all wasted because we've given the two points away."
Meanwhile, Ferguson expects captain Rio Ferdinand to return to the line-up for Tuesday's Champions League clash with Rangers.
"I think Rio will play on Tuesday night," he added of the 31-year-old, who has been sidelined with a knee injury sustained in England's first training session in South Africa before the World Cup.
"It's a European tie at home and we've got to take advantage of that."