Eden Hazard's first-half header proved the difference as Chelsea followed their Capital One Cup win with a victory which ensured their five-point lead over Manchester City remained intact.
It might have been different had the restored Thibaut Courtois not made a host of fine saves and Chelsea's defence, shaky at times, not made some key blocks.
"When good football is not enough, we fight, we suffer together, we cope with difficult moments," Mourinho said.
"It was not the best game to play after the final
The final is more than a game, because of tension, pressure and emotions.
"Some periods we had to defend with everything
It's a game where you easily can lose two points.
"We had chances to kill the game
We were expecting that.
"We didn't and when you don't do that against West Ham you are in permanent danger
Great victory for us."
West Ham manager Sam Allardyce contested Hazard's goal should not have stood.
"I've looked at the goal and it was offside," Allardyce said.
"Kevin Nolan was offside at Old Trafford (in September) when we scored for 2-2
There was half an inch of his nose offside and they said that was offside.
"There was about six inches of his (Hazard's) body offside this time and they said it's onside."
Mourinho dismissed Allardyce's complaint.
The Blues boss said: "Eden starts the action outside the box and he moves the ball, Fabregas, Oscar, pass to Ramires
I don't think Ramires is offside and Eden coming from outside the box I don't think is offside
But I didn't see on television
Maybe Sam saw it
For me, no.
"The only goal we scored is fantastic football
If Ramires scored that goal that he hit the post, it's fantastic football.
"If Willian scores the goal with an open goal it's fantastic football."
Mourinho, who has been critical of match officials this season, praised referee Andre Marriner and his team after an action-packed contest.
"This match must be a nightmare for a referee," he said
" For me Andre and his assistants had a good game."
Chelsea have one trophy this season and Mourinho hopes the quality of his side can deliver further success.
"Now we are trying to build
We have one cup in the pocket
Let's see what we can do," he added.
"What's kept us top of the league since day one is the quality of our football
(But) sometimes we lose a little bit what brought us to this position."
The loss of quality is when players are injured or suspended
On Wednesday night Nemanja Matic was both.
Matic was completing a two-match ban for his sending off against Burnley but would not have been fit to play after an injury in celebrating the League Cup win.
He had changed from his club suit to full playing kit for the trophy presentation at Wembley before twisting an ankle, but the midfielder will be fit for next week's Champions League last-16 second leg against Paris St Germain.
"Matic is injured and he got an injury celebrating the cup," Mourinho added.
"It's not a big injury, but if today he was not suspended, he wouldn't play.
"He twisted his ankle
On the pitch
He put on shinpads but he didn't put the tape on
He will play against Paris
On Saturday, Sunday, he will train."
Allardyce, who lost defender Winston Reid to a hamstring injury, rued the fact his side's run is now one win in 11 league games.
"I thought that we gave a fantastic performance today," he said.
"We really wanted something out of the game
We got a great performance and we've got to take a lot of positives out of that.
"Couldn't have asked for any more entertainment, everybody, I don't think
Terrific game of football.
"Just we're the wrong side of the result, sadly
Keep playing like that and we'll start winning again."
Source : PA
Source: PA