Goals from Michail Antonio and Lingard in each half dented Spurs' chances of finishing in the top four for the second consecutive season.
Lingard spent two-and-a-half years playing under Mourinho at Manchester United before the latter was sacked.
Lucas Moura's goal brought Spurs back into the match but the defeat means they are now nine points behind fourth place West Ham in the Premier League table.
"I am really enjoying my football," Lingard told BBC postmatch. "The lads have taken to me really well. Today we had to graft for the three points and we showed what we are capable of.
"I have been around a team winning trophies at Manchester United and I know about the winning mentality and what that can bring to the team. I have come here to play football. Football makes me happy and when we win."
The hosts opened the scoring inside four minutes when Spurs failed to deal with a Jarrod Bowen cross and Antonio was quickest to react.
The best chances for a Spurs equaliser came at the end of the first-half but Lukasz Fabianski denied Lamela and Kane with good saves.
There was a long delay due to a VAR check for offside but the goal stood as Lingard celebrated his third goal for the club since his loan move from Old Trafford.
Spurs got themselves back into the match just after the hour mark when Moura scored with a great header from Bale's corner.
Bale came close to scoring a sensational equaliser but his long range effort rattled the crossbar.
Son Heung-Min almost scored a stoppage-time equaliser but his attempt hit the post and West Ham managed to hold on for the win.
"It's disappointing because I think we played well and we lost because of our mistakes," Spurs forward Moura told Sky Sports.
"We worked hard and we showed a good effort. We just need to think now about the next game. It's missing something. But we need to look forward. There are a lot of games to play. We need to improve."