Alfredo Morelos' opener looked set to be sending Rangers into the knockout stages as Group G winners on Thursday, until Borna Barisic's own goal drew Young Boys level in the closing stages.
Ryan Jack then saw red in stoppage time, but Rangers held on as they joined group winners Porto – who triumphed 3-2 against Feyenoord – in qualifying for the last 32.
Gerrard was particularly pleased with the response from his players after their 1-0 defeat to rivals Celtic in the Scottish League Cup final.
"I'm very pleased that we will continue European football after Christmas," the Rangers manager said. "It took character and guts. It's been tough since the weekend. I know what it’s like to lose a final, you feel flat. You take days to recover.
"For us to recover and perform well enough to get out of the group is fantastic."
Rangers progressed from a tricky group, leaving Gerrard to reflect on the club taking "another step in the right direction" under his stewardship.
"I'm not going to stand here celebrating a draw, or finishing second, but let's give credit where it's due," he said. "This club has suffered a lot, I think this is the first time they've had knockout football in Europe since 2011.
"Eight years ago, they had top footballers and obviously it has suffered a lot. This is another step in the right direction. Very pleased, very proud but I won't over celebrate."
Gerrard also revealed he is close to signing a new contract with Rangers, having recently suggested terms had been agreed.
"Something's imminent," said the former England international who took over at Ibrox in May 2018.
"It's pretty straightforward. I've been waiting for this moment, to get the two huge games out of the way, and the club will announce it when they're ready.
"But for me now it's all about Motherwell, getting the lads recovered."