O'Neill insists Davis was a match for anything they faced.
"Steven in particular over the two games has been absolutely phenomenal. He could play for either Uruguay or Chile quite easily," said O'Neill.
"His level of ability, to stay on the ball, was exceptional. The rest of the players get belief from that.
"Steven has found a new gear this year in terms of fitness. He's embraced the challenge of playing in the Premier League as opposed to the SPL.
"It maybe took him a little bit of time to adjust from Scotland back to the Premier League but what he's shown in these games is that against world-class players he does not look out of place."
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