The Turkey global added his second six minutes from time with a diving header to give Everton victory over ten-man Stoke, who lost Charlie Adam to a first-half red card for a two-footed lunge on Wayne Rooney.
"I don't think you can be too reliant on one player", Lambert told a media conference. reports Goal.
The home side defied their numerical disadvantage to briefly halve the deficit through Choupo-Moting and inspire hope of a precious result in what was billed as the embattled club's biggest league game in 10 years.
Stoke were left fuming by the decision as they are in desperate need of points in their battle to avoid relegation from the top-flight and it came at a crucial point in the contest, just 34 minutes into the game.
The former Scotland worldwide was shown a straight red for catching Rooney with a studs-up challenge as both players stretched for the ball. Things really swinged in the Toffees' favour half an hour into the game, however, as Stoke midfielder Charlie Adam was sent off for a reckless tackle on Rooney.
Tosun looked to be in an offside position as he initially attempted to head home Yannick Bolasie's cross in the 69th minute, before burying the loose ball amid a subsequent goalmouth scramble.
Fortnite Steam: how to get the battle royale game on Valve's client
Like Overwatch or League of Legends, there is no Fortnite Steam version. unless you know this little trick, that is. Not to worry, though: below you can find out how to put Fortnite on your Steam account.
The Cameroon worldwide injured himself in the process and proceedings quickly went from bad to worse for Lambert, with Tosun stooping to head in Theo Walcott's cross in the 84th minute.
Stoke City striker Mame Biram Diouf has a "slight chance" to play against Everton in Saturday's Premier League encounter, according to manager Paul Lambert.
Tosun, a January signing from Besiktas who has four goals in his last three games, put Everton ahead in the 69th minute and, after Stoke equalised, scored the victor in the 83rd minute with a diving header from a cross from Theo Walcott.
Everton return to action on March 31 with a game against Manchester City at Goodison Park.
Tosun, 26, has scored two goals in his last two games against Burnley and Brighton after failing to find the back of the net against Tottenham Hotspur, West Bromwich Albion, Arsenal and Watford.
- Tosun also became the first Turkish player to score a Premier League brace since Tuncay Sanli for Middlesbrough against Aston Villa in November 2008.