Roberto Martinez admitted he was disappointed to take just a single point from the game at Stoke.
Everton hit the woodwork twice in the first half and dominated the second period after Oussama Assaidi had scored for the home side.
The Blues finally equalised in added time through Leighton Baines' nerveless penalty.
Martinez told evertontv: "I never felt that we didn't have a chance because the character of the team was immense.
"I knew that with the conditions of the weather and the way the game was being played that the first goal was going to be significant. We were very unfortunate to hit the crossbar twice and (when that happens) you feel it is not going to be your day.
"But I couldn't be happier with the reaction. I thought we were patient enough at times but penetrating enough too.
"Probably we should have got the three points rather than one but it is a positive result. It will seem a significant point at the end of the season."
The manager was deprived of first choice central defensive pairing Phil Jagielka and Sylvain Distin through injury, with John Stones and Antolin Alcaraz deputising.
Distin could be out for 10-12 days with his hamstring problem.
But Martinez praised the way Paraguayan Alcaraz has seamlessly slipped into the Blues defensive unit.
Martinez continued: "Antolin is getting the rewards for the hard work he has put in behind the scenes. I am pleased the fans are able to see what a fine player we have.
"The way he was talking and communicating with John Stones was very pleasing. They were ready to help the team and that gives me a great feeling of satisfaction."
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