The managerial duo resigned with immediate effect after the game, along with coach Alex Norwood.
And the Storks now hope to have a new man in charge for Saturday’s derby clash at home to high-flying Barnoldswick Town.
A Padiham statement, released on Sunday, said: “After yesterday’s first team defeat at Winsford United, immediately after the game, the management team of Liam Smith, Dixon Lambert and Al Norwood resigned from the club with immediate effect.
“Everyone at the club would like to pass on our thanks and gratitude to them, for the exceptional hard work they constantly put in for the club.
“We wish them all the best in whatever they decide to do in the future.
“The search for the next manager has already begun, and we will be welcoming applications for the vacant roles.
“Applications should be sent to [email protected]
“Hopefully, someone will be in place for Saturday’s home game against Barnoldswick Town.”
Smith himself explained the decision on social media: “After yesterday’s game we have decided to step down as a management team from our roles at the football club.
“The decision hasn’t been taken lightly, but recent results and performances have fallen short of the standards we have set and we feel it’s now time for the club to bring in somebody new with fresh ideas to take the club forward.
“I’m very proud to have managed the football club with two of my best mates who will be friends for life.
“I’d like to thank the players, past and present, the club, supporters, committee and all connected at Padiham FC for the opportunity and with you all the success in the future. UTS.
“Now I’m looking forward to a good break and spending much-needed quality time with my new little family.”
Padiham were beaten 4-1 at Winsford, as David Short hit a hat-trick for the hosts.
He netted on 14 minutes, and though Jack Tinning equalised on 36 minutes, Short scored again two minutes before half-time.
Winsford were reduced to 10 men after a poor challenge on Adam Jones, but Short completed his hat-trick, and George Blackwell made it 4-1, before Winsford collected a second red card.
It was a seventh game without a win for the Storks – of which they have lost five.
Smith and Lambert took over from current Northwich Victoria boss Steve Wilkes in September 2017.