The Blues were moments away from suffering a second straight Barclays Premier League defeat - which would have been a first at home for Mourinho - after the Baggies came from behind with two second-half goals.
There may be much debate around the decision of referee Andre Marriner to point to the spot after Ramires had gone to ground under what looked a fair shoulder challenge from Steven Reid, but Chelsea's spirit to press on until the very end as they secured a 2-2 draw could not be questioned.
"We played a serious game against a side who made it very difficult," said Mourinho.
"Then in the second half we were losing, and when you are losing you are under more pressure.
"But we had a good reaction with good character and in the end we never deserved to lose, so I can have no complaints with the boys."
Mourinho, though, did have issues with the overall officiating of the match.
The Chelsea manager felt there was a foul on Cesar Azpilicueta in the build-up to Stephane Sessegnon's strike on 68 minutes, which squirmed under goalkeeper Petr Cech.
"If someone has reason to be unhappy with the referee's performance it is us because the second goal almost killed the game and it was a big mistake by the referee," the Blues boss said.
"We have a reason to be upset with that but he is a good referee, one of the best in Europe.
"I am not happy with his performance but he is a referee I like very much."
It was a frantic end to a match which had failed to spark into life until the closing moments of the first half, with West Brom's high-pressing game limiting Chelsea's attacking chances.
The Blues, who lost at Newcastle last weekend, eventually went ahead though another poachers goal from Samuel Eto'o after defender Liam Ridgewell delayed his clearance following a fine save by Boaz Myhill from Hazard's angled drive.
However, West Brom were level on the hour when Shane Long, who had hit the post minutes before, got up above the Chelsea defence to head in from close range after Cech had kept out a bullet header from Gareth McAuley.
Hazard had made headlines earlier in the week when he was axed from the Champions League match against Schalke for returning late after a trip abroad because he had misplaced his passport.
The Belgian midfielder, though, showed great composure to stroke home what was a high-pressure spot-kick.
"He was cool," said Mourinho.
"It is difficult when you are losing and you have a penalty in the last minute of the game, so it is not easy to take in these kind of situations and he was very calm."
Mourinho, who returned to take charge at Stamford Bridge for a second spell earlier this summer, may have come within touching distance of what would have been a first defeat in 66 Premier League home games, but the Portuguese coach insists he would not be concerned to see such an impressive statistic consigned to the history books.
"When I lose my first match at home, I think that will be a moment to celebrate my record," he said. "It is not a moment to be disappointed because my record is not normal."
Azpilicueta was again preferred at left-back to Ashley Cole and Mourinho felt the Spaniard had once more shown his qualities before being replaced as Chelsea chased a positive result.
"We were losing so I had to take risks. I preferred to play with three defenders, the powerful guys in the air that could also be a threat in attack, so I sacrificed Azpilicueta, but he's played two very good games," said Mourinho, whose side are now in fourth place.
Mourinho had given West Brom boss Steve Clarke, his former Chelsea assistant, a kiss after the penalty went in.
The Portuguese coach is glad to see his good friend establishing himself in a first management role.
"Steve is a good coach. Defensively they are compact, well organised and committed, so they made it difficult for us," Mourinho said.
"He came here to get a result and they got one."