The Spurs boss was delighted with the side's first half performance as goals from Roman Pavlyuchenko and Luka Modric gave them a 2-0 half time lead.
However, Everton improved significantly after the break and after Yakubu pulled a goal back on 55 minutes Spurs were forced to defend for their lives to earn the three points.
"We were terrific at times in the first half and deserved our 2-0 lead," Redknapp said after the game on Sunday lunchtime.
"But, when you play Everton you know they are not going to give up.
"David (Moyes) obviously got into Everton at half time and they raised their game.
"They scored, came on strong and we became edgy.
"At 2-1 we were defending for our lives at timesbut overall I was delighted with the performance and the attitude of the lads."