It was confirmed after the match that the Argentine fractured the radial bone in his right arm and that he is expected to be sidelined for approximately three weeks.
Luis Suarez stretched Barcelona's lead from the penalty spot (63) before Pablo Sarabia's deflected shot reduced the deficit.
"We drifted out of the game after a good start to the second half and, instead of making it 2-0, we let them make it 1-1", Allegri said.
He had already assisted and scored by that point, with Barça eventually going on to win the game 4-2 to replace their Andalusian opponents at the top of La Liga.
More than 7,000 people headed for United States in migrant caravan
Hundreds of locals driving pickups, vans and cargo trucks stopped to let them clamber aboard. He said the migrants' rights must be protected as they break into Mexico and head north.
The 31-year-old landed awkwardly on his arm and a physio applied strapping before Ousmane Dembele came on as a replacement.
On Saturday night, Camp Nou saw hosts Barcelona beat Sevilla 4-2, ending a streak of four La Liga gameswithout a win.
Messi had already scored 17 goals in all competitions so far this season before his injury.
"It is clear that it is a sensitive low", Valverde told reporters.
"It makes a big difference to have or not to have him but we have enough cover so as not to worry about whether he is there or not".
Barca defender Gerard Pique admitted Messi's absence would have an impact on the team.
Madrid have now gone five games without a victory and when Marcelo gave them hope of a comeback at the Santiago Bernabeu, they had gone 481 minutes of normal time without a goal too.