Spurs had dominated the first half and looked to have won the match courtesy of Benoit Assou-Ekotto's deflected 75th-minute strike.
"It is difficult to take [the equaliser] in the last minute of the game," said Villas-Boas. "We have to keep our concentration.
"We had an extremely good first half and our idea was to get something out of this and therefore be a bit calmer in the second half.
"It is very, very important to get that first win but there are still 36 games ahead of us. We have one more point than we did this time last year.
Clarke praises West Brom character
"The players have been excellent. They have been receptive and there is a good feeling about what we are doing. We are just waiting for the results to accompany us a little bit more."
West Brom boss Steve Clarke was pleased with his side's second-half display, which saw them grow into the game and get a deserved leveller through Morrison.
"I think we deserved to get something from that game for our second half performance," admitted Clarke. "In the first half they controlled it but didn't make Ben Foster work too hard.
"We had more aggression in our play after the break, got forward and created chances and it would have been a shame if we hadn't got something from it."
Having taken over at The Hawthorns in the summer, Clarke's side are now unbeaten after two matches - having
won their opening game 3-0 against Liverpool
- and the former Chelsea and Liverpool head coach is happy with the way the Baggies are developing.
"I've inherited a good group of players," added Clarke. "I've tried to add one or two to help them and we are progressing nicely.
"We try to play when we can and we're competitive when we don't have the ball. If we keep playing how we did today we'll have a good season."
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