The Baggies found themselves 1-0 down at Old Trafford after just nine minutes, but had a number of chances to equalise in the second half before Robin van Persie's 90th-minute strike sealed a 2-0 win for United.
Clarke believes that his side played good enough football throughout the match to warrant a draw, reserving special praise for goalkeeper Ben Foster.
"There was a stage in second half when we had a really good control. I thought the game was more likely to go 1-1 than 2-0," said Clarke.
"Ben Foster made some good saves, that's why we spent our whole transfer budget on Ben in the summer. Some of the football we played was very good and I thought the goal would come.
"We had players on the pitch who can score and got into some good positions."
The result ensured that United will end the year seven points clear at the top of the Premier League table, while West Brom stay sixth.