Britton was in the dugout for the first time following the sacking of Paul Clement on Wednesday and saw Jordan Ayew’s thunderous 77th-minute strike cancel out Luka Milivojevic’s penalty.
It was the first time this season that Swansea – who will spend Christmas bottom of the Premier League and four points from safety – have taken a point from a game in which they have conceded.
“I was really pleased with the performance, I thought it was what we deserved,” Britton said. “We started well with a good tempo and it was disappointing we didn’t create more chances and take the lead.
“But the character we showed going 1-0 down was brilliant. I’m very proud for the efforts they gave me, not just today but over the last few days in difficult circumstances.
“We didn’t settle for a point after we scored, we kept pushing and if one team was going to score again it was ourselves.”
On whether he will be in charge at Anfield on Tuesday – with Swansea hoping to make a swift managerial appointment – Britton said: “I haven’t heard anything new.
“I spoke with the chairman (Huw Jenkins) and the owners on Friday, but I haven’t done so since the full-time whistle. We’re ready to be in training and prepare for Liverpool until I’m told anything different.
“I enjoyed the game as much as I could. There’s been a lot going on in the last couple of days and it’s all very new being out there in the technical area.
“I enjoyed it more because we had some form of result, but the full-time job is not something I’m looking to do on a permanent basis at this moment in time.”