Tosun looked to be in an offside position as he attempted to head home Yannick Bolasie's cross in the 69th minute, before burying the loose ball amid a subsequent goalmouth scramble.
Stoke, who had Charlie Adam sent off on the half hour, quickly equalised through Eric Maxim Choupo-Moting, yet parity only lasted seven minutes as Tosun returned to net the winner and heap more pressure on a home side stuck in the Premier League relegation zone with only seven games to play.
Lambert said he understood referee Martin Atkinson's decision to dismiss Adam, but the Potters boss was upset by the manner in which his team's dogged rearguard came undone.
"I thought the first goal was offside. Well it is offside because I have seen it," Lambert told the club's video channel.
"The thing that disappoints me most is that it is the linesman's side. He is looking right across the line. How he has not seen that is disappointing.
"The response with 10 men to going a goal behind was fantastic. I thought we were well in the game, but the first goal is offside.
"He has got to call that right. You cannot get that wrong. It gave Everton something to hang on to."
Conversely, Everton boss Sam Allardyce praised Turkey international Tosun for securing the Toffees a first Premier League away win in seven attempts.
"It looked a bit iffy for us again but Cenk popped up with a super goal and that is why we bought him," Allardyce said of the striker, a January signing from Besiktas.
"It has paid dividends for us and it puts us on the 40-point mark, and even though mathematically we are not safe I do not think anyone can catch us now and we can start to prepare for next season."