Harry Redknapp said a resurgent Everton produced the resolute performance he was expecting after Saturday's 1-1 draw at the Lane.
David Moyes' side arrived in N17 on the back of last week's Merseyside derby win and proved a tough nut to crack in a game of few clear-cut chances in the Premier League.
The goals arrived in the space of four minutes in the first half.
For the fifth league game running our opponents took the lead as Leighton Baines curled home a free-kick into the top corner from 20 yards with 17 minutes on the clock.
However, we struck back quickly when Peter Crouch and Rafael van der Vaart combined again, Crouch nodding Alan Hutton's cross across goal for the Dutchman to tap home his fourth goal in four games - all set-up by the big man.
We looked the more likely team to get the winner after that but struggled to cut open an Everton defence marshalled superbly by Phil Jagielka.
Luka Modric fired just wide, Crouch headed straight at Tim Howard and then shot across goal in the second half and Roman Pavlyuchenko saw another goalbound effort deflected just wide.
"It was as tough as I expected," said Harry.
"Everton are just starting to get on a roll, which they seem to do every season.
"They tend to have bad starts but they always end up in the top six or seven and I'm sure they will be up there again this season.
"We knew it would be a difficult game. Everton make it hard for you, get around you, they close you down, work hard and have that extra man in midfield with Cahill dropping in deep.
"He did that in the first half especially and you can get outnumbered in there. Heitinga also got around Rafa and obviously he knows him well from the Dutch team.
"They were never going to come here and make it easy for us and it was a good Everton performance away from home in a tight game."
Meanwhile, Harry said Tom Huddlestone missed out due to an ankle injury and that he substituted Wilson Palacios at half-time after the midfielder was booked early in the first half.
"I just felt if he made one more foul he might get sent off," added Harry. "But Sandro came on and did okay."