Spurs had to play for 80 minutes in Wednesday's 4-3 Champions League defeat to Inter Milan with ten men following goalkeeper Heurelho Gomes' red card and fell behind to Everton when Leighton Baines broke the deadlock with a superb free-kick.
However, Spurs gained a deserved point when Rafael van der Vaart equalised with a close-range finish and Redknapp thought it had been a performance of great character.
The Spurs manager said: "They're a good side and you're never get an easy game against them. I thought we had the better chances but it didn't quite drop for us.
"You want to win every game but what's important, when you're not going to win, is not getting caught out late on with the sucker-punch and end up getting beaten. Sometimes we've done that in the past, like against Wigan.
"But we stayed solid and the centre-backs were top-class. We've always showed good spirit and a never-say-die attitude.
"But I couldn't fault the effort of the players, we worked hard today. We just needed a break, but it didn't quite come.
"To come back again from 1-0 down shows a lot of character. We go behind and we come back, we never give up."