Despite the run of form, Redknapp said Spurs needed to concentrate on their league position as they aim to qualify for the Champions League next season.
"I'm not bothered about the run. We played well in the second half and we didn't do a lot wrong in the first half.
"[In the] Second half it was completely one-way traffic. We just couldn't get the goal that we deserved. I couldn't have asked for any more in the second half.
Moyes admits to fortune in victory
"We have to keep going. We've not been out of luck. We got
well beaten at Arsenal
- they battered us in the second half and we got what we deserved: nothing. Last week we played ever so well
against Manchester United
and we were unfortunate. Today we were unfortunate.
"But that's football. We've won games we shouldn't have won this year and you lose some that you shouldn't lose."
Everton boss David Moyes celebrated an upcoming 10-year anniversary at the club with a win which lifts his side to ninth in the table.
And it extends an unbeaten run to nine games, with Tottenham the latest big side to lose at Goodison after recent defeats for
Moyes said: "In the second half they put us under big pressure and we carried a wee bit of luck but sometimes you need that.
"It's never easy to come and play at Goodison and I hope none of the Everton teams I put out are easy to play against.
"They have a terrific team and played really well. Maybe [they are] the best team we've played at Goodison so far. That tells you what our players had to do to get a result."
Moyes also highlighted Jelavic's importance as the Croatian striker marked his first start for the club in memorable fashion since
signing from Rangers in January.
"What we've missed is the ball coming into the box. It's hardly even a chance really, and he takes it early," Moyes added. "We've not had that all season to give us a chance of maybe nicking games like we've done tonight."
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