The Australian international 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 common sense at the end, to see whether (Edwin) Van der Sar would have saved it or whether we would have scored, but it happens."
Toffees keeper 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."