The hosts carved out a number of chances in the first-half, with goalkeeper David de Gea forced into seven saves throughout the match.
“It was the whole first half. I said at half-time I was the luckiest manager in the Premier League in a half when it should be like 5/6-2,” Mourinho said.
"We were defensively awful. As a team we didn't press or do any of the work we did in the week.
“People watching this game will not believe how hard we worked this week.
Callum WIlson opened the scoring at the Vitality Stadium (Image: GETTY)
In-form Anthony Martial has scored five goals in his last four Premier League games (Image: GETTY)
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"The first half was a disaster. The second half was much better.
“We created lots of chances and deserved to score before the 92nd minute.
Mourinho’s decisions appeared to swing the momentum in his side’s favour after half-time.
Summer signing Fred seemed to struggle with the pace of the game and the Red Devils boss acted swiftly by bringing him off for Ander Herrera just ten minutes after the break.
Marcus Rashford scored a late winner for United (Image: GETTY)
When asked what he said to his players at half-time, Mourinho added: "I started off positive.
“I said it is impossible to play worse than we did so the second half will be better for sure. I was happy bringing Ander Herrera into the game.
"I felt we needed him to give more balance and to recover the ball faster. I was happy with that change. It was much better."