Villa slipped to a 2-1 defeat at Emirates Stadium on Saturday, with that setback dropping them back into the Premier League relegation zone.
Lambert's men held their own for long periods in north London, though, and saw Andreas Weimann cancel out Santi Cazorla's early opener.
Cazorla pounced again late on to snatch all three points for the hosts, and Lambert feels the final result was harsh on his battling troops.
He told Sky Sports: "I don't think we deserved to come away from here losing, but we did. I can't fault the lads for the way they played, I thought they were excellent.
"I thought we should have scored more than one goal. The way we played was very, very good."
Villa have won only one of their last 10 in the league, but Lambert believes they are offering enough to suggest they are capable of preserving their top-flight status.
He added: "If we keep playing like that, we will see what happens.
"We have been playing well for a number of weeks. We have been beat, but the performance we will take great, great heart from it.
"Every game we need to play at that level. We are certainly playing well enough, that's for sure."
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