Lalkovic scored one goal and then set up Romaine Sawyers for the second as the Saddlers bounced back from successive 1-0 league losses and inflicted a third straight league defeat on Posh, who had defender Shaun Brisley sent off for a second bookable offence in the 77th minute.
It was a brilliant display by Smith's side, and they even missed a last-minute penalty when substitute Ashley Hemmings saw his effort saved by Bobby Olejnik.
"It's been Milan's first taste of league football with us, and its been a bit of a stop-start season for him because of international commitments with the Slovakian Under-21 team, and he's learning the game, but he and Romaine Sawyers are learning quickly,`` said Smith, whose team are now seventh in the table and only one point shy of a play-off spot.
"His contract with Chelsea is up at the end of the season and he wants to set his career path on the right track.
"It was a really good performance by all our players, both goals were well worked and the only disappointment was that we didn't score more. But when we play like that we can beat anybody."
Lalkovic said: "This is the performance I can do and this team play good football. I want to extend my loan until the end of the season then see what happens. I think I can help this team achieve something."
Peterborough manager Darren Ferguson admitted the best team won on the night.
"Walsall are a very good team. I thought we were well beaten and I have no complaints - it could have been more than 2-0,`` said Ferguson, whose side stay third in the table but are now six points behind second-placed Leyton Orient and a further point adrift of league leaders Wolves.
"Shaun Brisley was sent off for a silly tackle when he was on a yellow card. It was a silly challenge.
"A third of the season has gone and I have seen certain things and inconsistencies, and in areas of the pitch we have not been good enough. It's up to me to get our form back and there's no question in my mind, I know what I want to do.
"I have to be honest and say there have certainly got to be changes.``