The Scot refused to say where he was when Leon Osman deflected in Royston Drenthe's shot nine minutes from time to equalise Grant Holt's 28th-minute opener. But even though it meant his side left Merseyside for the second time in two months with a point - having drawn at Anfield in October - Lambert was satisfied with the outcome.
"This is a really hard place to come and we battled really strongly and defended really strongly when we had to but also looked a threat," he said
"They came rolling right at us and you weather the storm, that is what you have to do and that is what we did at Anfield.
"Any point away from home is good."
Everton boss David Moyes felt his side deserved to win, having dominated for long periods, but was thankful to escape with a draw after two successive defeats.
"I thought we had played well," he said. "We didn't score but for 25 minutes we played well and our worst period was after they scored in the 15 minutes up to half-time because it took the wind out of our sails.
"I don't think we were getting battered but it was a really poor goal we lost and it presented another mountain to climb.
"For a long time it didn't look like we could get a point out of the game but thankfully we got a point - but we deserved three.
"The boys played well but didn't have the bit at the top end to get us a goal."
Source: PA
Source: PA