A Christian Benteke penalty was not enough to cancel out a two-goal half-time deficit as Villa fell to a fifth defeat in seven games.
The result means Villa drop into the relegation zone but Lambert praised his side's second-half display and has promised that they will battle hard to turn around their recent form.
He said: "There will be a few teams down there and we will have to fight our way out of it.
"I've never seen a standing ovation after getting beat before but that shows the effort we put in in the second half. We never played well in the first half all but I couldn't fault them after the break."
Earlier this week, Villa owner Randy Lerner revealed that Lambert would not have great financial backing before the close of the transfer window and thus the Scot appeared negative when asked over the prospect of arrivals in the coming days.
Lambert added: "Money dictates everything and the situation hasn't changed. I don't know if we will be able to bring anyone in, let's see what the next two days brings.
"You have to survive in the league and sometimes you need a bit of help."
Villa return to Premier League action on February 10, when they travel to Everton.