Argentine striker Lautaro Martinez scored a well-worked equaliser to cancel out Ramos's opener for the Mexican side in front of 40,311 fans at the Rose Bowl.
Inter, playing their first game since being thrashed 5-0 by Paris Saint-Germain in the Champions League final, were left ruing their failure to turn their dominance of possession and territory into goals.
But the draw was a boost for Ramos and Monterrey, who face Argentina's River Plate in their next game on Saturday.
"When you don't get all three points you're never entirely happy," Ramos, the former Spain and Real Madrid defender, said.
"But one point is better than no point.
"They were a tough opponent and have just played in the final of the Champions League. We were a little bit nervous but in the second half we stayed organised and kept the ball better.
"Now we need to think about the next game."
Inter coach Cristian Chivu said his team had struggled to break down a Monterrey team who sat deep for long periods.
"We played well in the first half even though we went behind," Chivu said. "We could have attacked better in the second half. It's not easy to play against a very low block."
Chivu, in his first match in charge after the departure of Simone Inzaghi, denied the Champions League finalists had underestimated the Mexicans.
"We respect every team we play and we knew what kind of team they were, we tried to do our best," he said.
"Sometimes you get the best out of it, sometimes you don't. We created a lot of chances. Football's not won on paper."
All Inter
The Italians were in complete control almost from the kick-off, Benjamin Pavard the first to threaten with an eighth-minute shot that flew over the bar.
Matteo Darmian should have done better in the 22nd minute but shot over after clever work down the left from Nicolo Barella.
Yet despite the early onslaught, Inter were rocked in the 25th minute when Monterrey scored from one of their few forays into the Italians' half.
Midfielder Oliver Torres swung a corner in from the right and Ramos -- who had lost Francesco Acerbi on the edge of the six-yard box -- steered his header into the bottom corner.
Inter were soon back on the offensive and only a point-blank save by Monterrey goalkeeper Esteban Andrada from Sebastiano Esposito prevented an equaliser.
Martinez also went close after 36 minutes, and Inter had a strong penalty appeal when Pavard's header struck Ramos on the arm inside the area.
VAR found in favor of Ramos and Monterrey escaped.
Three minutes later Inter drew level with a wonderfully worked free-kick routine.
Albanian international Kristjan Asllani shaped to shoot from 25 yards out but instead flighted a delicate chip behind the Monterrey defence.
Brazilian international Carlos Augusto timed his run to perfection and squared into the path of Martinez, who tapped in for 1-1.
Monterrey almost regained the lead against the run of play on 64 minutes, Sergio Canales unleashing a low shot that cannoned off the post.
Inter had a Martinez goal ruled out for offside moments later as the Italians continued to threaten.
But it was Monterrey who came closest to grabbing a winner in stoppage time when Colombian midfielder Nelson Deossa got behind the Inter defence but could only shoot into the side netting.
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