Julio Cesar's own goal cancelled out Junior Hoilett's early opener for Rangers, but Everton, and Jagielka in particular, had to defend desperately at times after they had Pienaar sent off in the 61st minute.
"It shows the spirit we've got, we dug in," the England centre-back told Sky Sports 1.
"Once we went down to 10 men I thought we did a very good job and limited them to very few chances."
Everton captain Phil Neville felt his side deserved their point.
"I think so," he said. "With Steven Pienaar getting sent off it was backs to the wall. We knew QPR were going to be fighting for their lives.
"I think when we went down to 10 men we would have taken a point."
Pienaar was dismissed for a second yellow card for a soft-looking foul on Jose Bosingwa.
"I think the second booking was a little bit harsh," added Neville.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
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