The 2-1 reverse in the third-round cup tie - against Sky Bet League One opposition - was Villa's fifth defeat in their last seven games in all competitions.
And it was yet another disappointing day at Villa Park in a campaign in which their home record so far shows just two victories and six losses from 10 top-flight fixtures.
There were boos from Villa fans at the final whistle and Lambert has expressed his understanding for their frustration.
But the Scot - under whom Villa finished 15th in the Premier League last season, his first in charge of the club - has also emphasised how important he feels it is that the supporters do all they can to help the players.
"I don't have any problem with the crowd," Lambert said.
"If the team is not performing, then you expect people to vent their frustration - that is normal.
"But we are a young side.
"Last year, we played Newcastle at home and we were getting beaten 2-0 in the first half.
"Then we scored, and for about 40 minutes, it didn't matter what we did, that crowd was right with us. They were brilliant that time.
"Because you are in your second year, it might be a different view, but if they can stick with it and see us through the hard times when we need them... because we certainly need them.
"They have been excellent for us overall, and we expect if we are not performing that certain things will happen.
"But we're hoping (in the Arsenal game) that they will get right behind us."
Lambert said after a 1-1 home draw with Swansea in December that although he has a good relationship with his chairman Randy Lerner, he does not feel immune from the sack and always works with "that fear" of losing his job.
Returning to the theme this week, Lambert said: "I never stop worrying. I'm not immune from it.
"The relationship between me and Randy is what it is. You are never immune from anything, and I would never view it that way.
"You just keep going - there is no secret formula to it. You just keep going and don't lose focus on what you are trying to do. I will never waver from that."
- Sports & Recreation