Gylfi Sigurdsson gave the home side a 13th-minute lead at the Liberty Stadium, and Villa were unable to find a leveller, although they were much improved after the interval.
Lambert believes his side are progressing with every game and says Villa deserved at least a share of the spoils in south Wales.
"We're proud of them for the way we played," he said. "We've probably done to Swansea what they do to most teams coming here.
"I thought we worked past them, we hemmed them in - I think the way we're playing at the minute is really pleasing.
"We've changed the way we play and the lads are enjoying their football.
"Sometimes when you lose you can hold your hand up and say 'okay, we never deserved anything'.
"I go away from here disappointed to lose, but I'm delighted with the way we're playing at the minute."
Sigurdsson's opener came courtesy of a well-struck 20-yard free-kick that wrong-footed Brad Guzan, but Lambert refused to blame his goalkeeper.
"I think Brad will probably be disappointed, but there's no attachment of blame from my end," he added.
"Brad's made fantastic saves for us in the past and he'll make them again in the future."
Aston Villa next host Sunderland in the Premier League on Sunday.
