Could I have achieved checkmate with a King , Knight and Rook?

In this game, I was playing Black and ended up with a King, Knight and Rook but couldn't find a way to convert it to a win. I spent the last several moves just moving around the board trying to force Whites King into a corner where I would try to checkmate it. 

My opponent graciously accepted a draw when I offered it. 

I've played several games now where I am well up in material but struggle to inflict the final blow.   

Yes you can give checkmate here. In fact, probably the simplest thing to do is forget about the knight completely and just use the king and rook together to give checkmate. Do you know how to do this? eg.

Just a random position, but you restrict the king to a certain rank or file using your rook, then bring your king forward to face it. Use your rook to 'gain a move' if they keep avoiding the position with the Kings directly opposite one another. When the Kings are opposite give check, then repeat this process until the lone king is on the edge of the board and cannot escape checkmate by the same idea. 

https://www.chess.com/terms/chess-rook-king-checkmate

Thank you very much for that. 

Endgames is something I need to work on, though I'm very new to chess (been playing for about six weeks in total) and am trying to take all aspects of the game in. 

Up to now most of my opponents have either beaten me, resigned or offered a draw (or one of us has caused draw by stalemate, which I was trying to avoid in this one). 

Sometimes I sac my minor pieces just to simplify to a rook king or queen king ending.  It's lazy but lower risk of stalemate

Actually, giving checkmate with just a rook is possible, not even needing the knight. In an actual game, it will depend on how much time you have, it typically takes longer than some other checkmates. 

I think I was worried about my Knight being captured and thought I might then really struggle. It's been another learning curve.