Lambert took over from Gary Bowyer at Ewood Park on 15 November, with Rovers in 16th place in the table on a run of two wins in 10 games.
It was the 46-year-old's first appointment since his departure from Premier League Aston Villa in February.
"Today is a marker, we can win games," Lambert told BBC Radio Lancashire.
"If we hadn't conceded, then it would have been a perfect game.
"We played terrifically, there was a great atmosphere in the stadium and we scored two goals against a team that hasn't conceded in six games, so the team deserves credit for that.
"We looked threatening every time we went forward."
Jordan Pickford's own goal and a Jordan Rhodes spot-kick were enough to seal victory, despite of a late Joe Garner goal.
The loss of Tom Lawrence to injury in the first half was the only sour note for Lambert, prompting an early reshuffle.
"I've asked the players to do a lot for me this week, I think it was a bit of tiredness," the former Colchester, Norwich and Villa boss added.
"That could have been because of training, but if we don't train at intensity then we won't get up to speed.
"These little things will happen or might occur but sometimes you need to make a sacrifice. You might get a knock or strain, but hopefully Tom Lawrence has just got a knock."
Paul Lambert says his return to management with Blackburn Rovers was "almost perfect" after Saturday's 2-1 Championship win at Preston.