Alex Ferguson's 26-year reign at United came to an end with a thrilling 10-goal game at the Hawthorns, in which the visitors held a three-goal lead on two occasions.
However, half-time substitute Romelu Lukaku netted his hat-trick goal in the 86th minute to complete a sensational West Brom comeback, and Clarke said his side could have actually snatched three points.
He said: "The game was incredible, it must have been fantastic to watch. 
"Manchester United showed why they were champions, they were absolutely irresistible. 
"But this group of players know how to get results and our goal just before half-time was crucial.
"We dug in and pulled it back to 5-3 and from there we chased the game really well and created a lot of chances. 
"For a five-minute spell near the end I thought we were going to nick it, which would have been incredible.
"I think having been 3-0 and 5-2 down, though, we are happy to take a point."
Clarke also said that the enthralling match was a fitting result for Ferguson’s 1500th and final game in charge of Manchester United.
"It was a great occasion for Alex, he will always remember that game," he added. 
"I think anyone who was in the stadium today will remember it for years to come."