Villa were the better of the two sides for much of the 90 minutes at Villa Park and quite possibly could have taken all three points if they played with more efficiency in the final third.
Nevertheless, Lambert was buoyed by his side and feels that their confidence has lifted with some consistent victories to reward the fans just around the corner.
"I always gauge things by the crowd and I can really sense the supporters want us to do well," the former Norwich City boss said.
"The lads are only young and they will make mistakes like everyone else but the crowd are right behind us.
"We are slowly and surely getting there. I am not long in the door here - but we are doing everything we can to make the club a success.
"We can only do our best. The lads have been absolutely brilliant for me. I have nothing but pride in them."