Canaries' boss hails his side's fighting spirit to earn a point on their travels, and also praises captain Grant Holt after his first-half goal at Goodison Park
Grant Holt's opener was cancelled out late on by Leon Osman, but Lambert was happy to come away with a point.
He told reporters after the game: "We’ve come to a really hard place to come and we battled really strongly and defended strongly when we had to and looked a threat.
"I knew it’d be hard with the crowd that Everton have got, that drives them on and a team that wasn’t that long ago in the Champions League.
"They came roaring right at us and they’re a really good side. You weather the storm which you have to do and it was the same at Anfield, they came at us and we defended strongly and got ourselves a point there and it was similar today."
Captain Holt followed up his goal-scoring exploits last week against Newcastle with another goal this afternoon, and Lambert is delighted with how he has stepped up to the Premier League alongside strike partner, Steve Morison.
"He’s been great for the last two and half years I’ve been here," Lambert continued.
"I think he’s scored 50-odd goals in a 100 games and in anybody’s book that’s a phenomenal goalscoring ratio. He’s always been a handful and it’s great testament to him.
"It was a brilliant finish; his hold-up in the box was excellent. He’s done it in League One and then the Championship and he seems to be doing it again.
"I just thought the lads deserved another go for what happened against Newcastle, the team picked itself basically.
"I thought we played really well against Newcastle and coming here we gave it a go, we tried to do everything we could to win.
"We’ve come to a ground where very rarely do Everton lose and I thought we hung in strongly to see the game through and if you said to me before the game we’d have got a point, we’d be okay. I’m delighted. Any point away from home is a huge, huge point."
Lambert was quick to praise goalkeeper John Ruddy, a former Everton player, who produced a fine series of saves that looked to have thwarted the Toffees' comeback chances.
He beamed: "I thought Tierney’s block he made in the box was different class and Kyle [Naughton] and John [Ruddy] I thought the back five were excellent when they had to.
"[John Ruddy] had nothing to prove to me, it's great for him to come back to the club that reared him and he probably has a lot of friends here but he’s been excellent for us."