Gibbs believes that Arsenal can take plenty of positives from their display against United, which stretched their unbeaten run to eight matches.
He told the club's official website: "Over the 90 minutes, I felt we were a lot better in the first half. Apart from some counter-attacks in the second half [when United looked dangerous], we're the ones who should be disappointed not to get the three points.
"We looked a bit tired [in the second half]. I felt that we dominated the first half. It was difficult for us to find our feet in the second half but all credit to the team, we gave everything to try and get the win.
"The team have responded to the position that we were in a few months ago. No one thought that we were capable of making that spot and now, with three games left, it's well within our grasp. We have to show what we've been doing in the last few months and take that into the last three games."
A London derby with Queens Park Rangers is next up for Arsenal on Saturday evening as they bid for Champions League qualification.