Christian Benteke scored twice and Gabriel Agbonlahor also found the net to help Villa carve out a 3-1 lead at Goodison Park, but a Marouane Fellaini double salvaged a share of the points for Everton.
The final goal came in the 90th minute and Lambert admits his men must stop dropping points from winning positions.
However, he took plenty of encouragement from Villa's display and praised his players for working so hard.
Asked for his feelings, Lambert told Sky Sports: "A bit mixed.
"I thought we played excellently. Nobody gave us an absolute earthly (chance) coming here. But our form against Newcastle was excellent and I thought today we were very, very good.
"Everton will come at you really strong and Fellaini has done that a number of times since he's been there."
Asked if he feared the worst when six minutes of stoppage time were signalled, Lambert added: "The lads gave us everything. They blocked it and I can't praise them highly enough, but you know what is coming."
"I think you have to see the game through. I think our form certainly looks good."